Department of Mathematics at UTSA - User contributions [en]

MAT1133

2020-12-16T18:27:28Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T18:20:32Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T18:16:42Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T18:09:48Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T18:02:04Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:57:22Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:54:39Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:53:17Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:45:29Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:41:22Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:26:16Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-16T17:13:42Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-15T22:41:41Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-15T22:39:34Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-15T22:23:21Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-15T22:09:33Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-15T22:08:51Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-15T22:07:10Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-14T18:18:26Z

Zachery.sharon: /* Topics List */

MAT1133

2020-12-14T18:17:46Z

Zachery.sharon: /* Topics List B */

MAT1133

2020-12-14T18:16:39Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Properties of Functions]]
* [[Toolkit Functions]]
* [[Graphs]]
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]]
* [[Linear Equations]]
* [[Properties of Functions]]
* [[Linear Functions]]
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]]
* Solving [[Quadratic Equations]]
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Graphs]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Functions]]
* [[Graphs]] of Functions
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- [[Solving Equations]]
:- [[Factoring Polynomials]]
:- Reducing Fractions
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits]]
* [[Rates of Change]]
* [[Graphs]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Rates of Change]]
* [[Limits]]
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T18:05:44Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]]
* [[Linear Equations]]
* [[Properties of Functions]]
* [[Linear Functions]]
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]]
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Graphs]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T18:03:22Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Linear Functions]]
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]]
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]]
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Graphs]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T18:01:16Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Linear Functions]]
* Fundamentals of [[Polynomials]]
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* Fundamentals of [[Polynomials]]
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Graphs]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T17:59:27Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* Fundamentals of [[Polynomials]]
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Graphs]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* [[Properties of Functions]]
* [[Domain]]
* [[Range]]
* [[Toolkit Functions]]
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T17:55:58Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* [[Properties of Functions]]
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T17:55:13Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Graphs]]
* [[Limits]]
* Graphs of Functions
*
* List:
:- List items
:- List items
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T17:45:22Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T17:43:57Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 0
||
* #
||
* [[Template]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* outcomes.
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Find average rates of change for function.
* Solve real-world problems involving average and instantaneous rates of change.
* Find instantaneous rates of change.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Find the line tangent to a function at a given point with the derivative provided
* Identify features of the graph of a function given information about the derivative.
* Identify features of the derivative of a function given information about the graph of the function.
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power rule.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Find derivatives using the generalized exponential rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Find derivatives using the generalized logarithmic rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* The First Derivative Test
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-14T17:29:38Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 0
||
* #
||
* [[Template]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* outcomes.
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Determine the vertices of parabolas and whether they open up or down.
* Graph parabolas.
* Find the equation for a quadratic function given the vertex and a point.
* Find the intercepts of quadratic functions.
* Solve real-world problems involving quadratic functions.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find limits using graphs.
* Find limits numerically.
* Use limit properties to find limits.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Find one-sided limits using graphs.
* Find limits involving infinity using graphs.
* Find limits involving infinity numerically.
* Use properties of limits to find limits involving infinity.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find the line tangent to a function at a given point with the derivative provided
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-11T20:01:45Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 0
||
* #
||
* [[Template]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* outcomes.
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Graph linear and piecewise-linear functions.
* Graph absolute value functions.
* Graph radical and polynomial functions.
* Determine whether a graph represents a function.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Solve real-world problems involving cost analysis and rates of change.
* Find the intersection point of two linear functions.
* Solve real-world problems involving break-even points as well as supply and demand.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find the line tangent to a function at a given point with the derivative provided
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-11T19:58:27Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 0
||
* #
||
* [[Template]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* outcomes.
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* Determine a table or equation defines a function.
* Find the domain of a function.
* Evaluate Functions for numerical values.
* Evaluate Functions for algebraic values.
* Find the difference quotient for a function.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 1
||
* 3.3
||
* Applications of [[Linear Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find the line tangent to a function at a given point with the derivative provided
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-11T19:53:46Z

Zachery.sharon: /* Text */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyLab Math with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyLab Math (MLM) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 0
||
* #
||
* [[Template]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* outcomes.
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 1
||
* 3.3
||
* Applications of Linear Functions
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find the line tangent to a function at a given point with the derivative provided
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-11T19:52:59Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyMathLab with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyMathLab (MML) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 0
||
* #
||
* [[Template]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* outcomes.
|-
|Week 1
||
* 3.1
||
* [[Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 1
||
* 3.2
||
* [[Graphs of Functions]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 1
||
* 3.3
||
* Applications of Linear Functions
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 3.4
||
* [[Quadratic Functions]] and Applications
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.1
||
* [[Limits]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 2
||
* 11.2
||
* [[One-Sided Limits]] and [[Limits Involving Infinity]]
||
* [[Link]]
* Item
* List:
:- List items
:- List items
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find the line tangent to a function at a given point with the derivative provided
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
|}

MAT1133

2020-12-11T19:37:31Z

Zachery.sharon: /* Topics List A */

==Course Catalog==
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1133. Calculus for Business]. (3-0) 3 Credit Hours. (TCCN = MATH 1325)

Prerequisite: [[MAT1053]] with a grade of "C-" or better, or an equivalent course, or satisfactory performance on a placement examination. This course is the basic study of limits and continuity, differentiation of single and multivariable functions, optimization and graphing, and integration of elementary, single variable functions, with an emphasis on applications in business and economics. May apply toward the Core Curriculum requirement in Mathematics. (Credit cannot be earned for both MAT 1033 and MAT 1133.) Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.

==Text==
In this course, you will use MyMathLab with this text: Mathematics with Applications 12th ed. Lial, Hungerford, Holcomb. The physical book is not required since MyMathLab (MML) has the text available in a digital format.

==Topics List A==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 3
||
* 11.3
||
* [[Rates of Change]]
||
* [[Function Notation]]
* [[Graphs]] of Functions
* [[Weighted Average]]
* [[Function Evaluation]]
* [[Equation of a Line]]
* Algebraic manipulations:
:- Distribution
:- Like terms
:- Factoring
:- Cancellation of Factors
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
|-
|Week 3
||
* 11.4
||
* [[Tangent Lines]]
||
* [[Limits of Functions]]
* [[Rates of Change]]
||
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find the line tangent to a function at a given point with the derivative provided
|-
|Week 3
||
* 11.4
||
* [[The Derivative as a Function]]
||
* [[Tangent Lines]]
||
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|Week 4
||
* 11.5
||
* [[Techniques for Finding Derivatives]]
||
* [[The Derivative as a Function]]
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
|-
|Week 4
||
* 11.6
||
* [[Derivatives of Products and Quotients]]
||
* [[Techniques for Finding Derivatives]]
||
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|Week 6
||
* 11.7
||
* [[The Chain Rule]]
||
* [[Composite Functions]]
* [[Function Evaluation]]
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Exponential Functions]]
||
* [[The Derivative as a Function]]
* [[Exponential Functions]]
||
* Find derivatives of exponential functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 6
||
* 11.8
||
* [[Derivatives of Logarithmic Functions]]
||
* [[The Derivative as a Function]]
* [[Logarithmic Functions]]
||
* Find derivatives of logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
|-
|Week 7
||
* 12.1
||
* [[Local Extrema]]
||
* [[Derivative Properties]]
* [[Simplifying Radicals]]
* Finding [[Domain]] and [[Range]] of a function
||
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|Week 7
||
* 12.2
||
* [[The Second Derivative]]
||
* [[Local Extrema]]
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
|-
|Week 8
||
* 12.3
||
* [[Optimization Applications]]
||
* [[The Second Derivative]]
||
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|Week 9
||
* 12.4
||
* [[Implicit Differentiation]]
||
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
|-
|Week 9
||
* 12.5
||
* [[Related Rates]]
||
* [[Implicit Differentiation]]
||
* Solve problems involving related rates in a variety of real world problems.
|-
|Week 11
||
* 13.1
||
* [[Antiderivatives]]
||
* [[Techniques for Finding Derivatives]]
* [[Derivatives of Products and Quotients]]
* [[The Chain Rule]]
* [[Derivative Properties]]
* [[Derivatives of Exponential Functions]]
* [[Derivatives of Logarithmic Functions]]
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
|-
|Week 11
||
* 13.2
||
* [[Integration by Substitution]]
||
* [[Antiderivatives]]
||
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|Week 12
||
* 13.4
||
* [[Definite Integral]]
||
* [[Graphs]] of a function
* [[Area]] of rectangles, triangles, and trapezoids.
* [[Antiderivatives]]
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 12
||
* 13.5
||
* [[The Fundamental Theorem of Calculus]]
||
* [[Definite Integral]]
||
* Apply the fundamental theorem of calculus to find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 13
||
* 13.6
||
* [[Applications of Integrals]]
||
* [[Definite Integral]]
* [[Elasticity of Demand]]
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|Week 15
||
* 13.7
||
* [[Differential Equations]]
||
* [[Antiderivatives]]
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|}

==Topics List B ==
{| class="wikitable"
|-
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|3.0
||
* 11.3
* 11.4
* 11.4
||
* Rates of Change
* Tangent Lines and Derivatives
* The Derivative as a Function
||
* Function notation, graphs of functions, limits of functions, the concept of a weighted average.
* Function evaluation, average rate of change, distribution, like terms, factoring, cancellation, finding the equation of a line.
* Limits. Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation.
||
* Describe the average rate of change of a function in terms of its algebraic meaning and geometric meaning.
* Describe the instantaneous rate of change of a function and its relationship to average rate of change.
* Find average and instantaneous rates of change in a variety of real world applications, including the velocity of an object moving in a straight line.
* Find the derivative of a function at a given point using the definition.
* Find the line tangent to a function at a given point with the derivative provided
* Find the slope of the tangent line and the equation of the tangent line to the graph of a function at a given point.
* Apply the concept of the derivative at a point in a variety of real world problems.
* Find the derivative of a function using the limit definition.
|-
|4.0
||
* 11.5
* 11.6
||
* Techniques for Finding Derivatives
* Derivatives of Products and Quotients
||
* Algebraic manipulations and basic understanding of exponents.
* Algebraic manipulations, e.g. distribution, like terms, factoring, cancellation of factors. Awareness of common pitfalls, e.g. inappropriate cancellation, improper distribution.
||
* Find derivatives using the constant rule, power rule, constant times a function rule, and sum-or-difference rule.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P
* Find derivatives using the product rule and quotient rule.
* Apply understanding of derivatives to solve real world problems involving marginal average C/R/P
|-
|5.0
||
* 11.7
||
* The Chain Rule
||
* Composite functions, function evaluation.
||
* Find derivatives using the chain rule and generalized power and exponential rules.
* Apply understanding of derivatives to solve real world problems involving composition of functions.
|-
|6.0
||
* 11.8
* 12.1
||
* Derivatives of Exponential and Logarithmic Functions
* Local Extrema
||
* Basic understanding of exponential and logarithmic functions. The mechanics should be accessible to students with a weaker grasp on these functions.
* Tangent lines and the derivative as the slope of a graph at a point, and derivative properties. Finding roots of functions and solving algebraic equations as well as domain and function evaluation.
||
* Find derivatives of exponential and logarithmic functions, including composite functions.
* Apply understanding of derivatives to solve real world problems involving marginal C/R/P, marginal average, C/R/P, and composite functions.
* Understand the connection between the derivative and a graph's increasing/decreasing pattern.
* Find the intervals on which a function is increasing/decreasing.
* Find the critical points of a function.
* Find the local extrema of a function.
* Use local extrema to solve real world problems.
|-
|7.0
||
* 12.2
* 12.3
||
* The Second Derivative
* Optimization Applications
||
* Domain of a function, derivative of a function, finding the roots of a function, solving algebraic equations, function evaluation.
* Domain of a function, the connection between a function's graph and derivative as well as finding roots of a function and function evaluation.
||
* Find the second derivative and higher-order derivatives of a function.
* Identify the intervals on which a function is concave up and concave down.
* Find the points of inflection of a function.
* Use second derivatives to solve real world problems, including finding the point of diminishing returns.
* Use the Extreme Value Theorem to find absolute extrema of continuous functions on closed intervals.
* Use the Critical Point Theorem to find absolute extrema of continuous functions on non-closed intervals.
* Solve optimization problems in real world contexts.
|-
|8.0
||
* 12.4
* 12.5
||
* Implicit Differentiation
* Related Rates
||
* Understand both what the chain rule says and how to use it, composite functions, derivative properties.
* The derivative as a rate of change, substitution, general problem reading/solving skills.
||
* Find derivatives of implicit functions.
* Solve problems involving related rates in a variety of real world problems.
|-
|9.0
||
* Case Study 11
||
* Elasticity of Demand
||
* Implicit differentiation, demand curves.
||
* Solve problems involving elasticity of demand in a variety of real world problems.
|-
|10.0
||
* 13.1
* 13.2
||
* Antiderivatives
* Integration by Substitution
||
* Derivative properties, substitution, and algebraic manipulations.
* Derivatives, the chain rule, composite functions, substitution, and algebraic manipulations.
||
* Find antiderivatives of functions using the power rule, exponential function rule, logarithm rule, constant-multiple rule, and sum-or-difference rule.
* Find antiderivatives involving real world contexts.
* Find differentials of various functions.
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
|-
|11.0
||
* 13.4
* 13.5
||
* Area and the Definite Integral
* The Fundamental Theorem of Calculus
||
* The graph of a function, areas of rectangles, triangles, and trapezoids.
* Antiderivatives, function evaluation
||
* Use numerical integration technology to calculate definite integrals.
* Apply understanding of definite integrals to solve real world problems.
* Apply the fundamental theorem of calculus fo find definite integrals.
* Find the area between the graph of a function and the x-axis on a closed interval.
* Apply understanding of definite integrals to solve real world problems.
|-
|12.0
||
* 13.6
||
* Applications of Integrals
||
* Area under a graph, graphs of functions, finding the point where two graphs intersect. Supply and demand curves.
||
* Find the area between the graphs of two functions.
* Find the consumers’ surplus and producers’ surplus.
* Apply understanding of definite integrals to solve real world problems.
|-
|13.0
||
* 13.7
||
* Differential Equations
||
* Antiderivatives, function evaluation, differentials
||
* Find general solutions to separable differential equations.
* Find particular solutions to separable differential equations.
* Solve real-world problems involving exponential growth and decay models.
|-
|14.0
||
* 14.1
* 14.2
||
* Multivariable Functions
* Partial Derivatives
||
* Function evaluation, domain, graphs of functions.
* Derivatives, substitution, marginal analysis.
||
* Evaluate a function of two variables.
* Find the domain of a given multivariable function.
* Apply understanding of multivariable functions to real world problems.
* Match graphs to equations.
* Find partial derivatives.
* Interpret first-order partial derivatives as a rate of change.
* Apply understanding of partial derivatives to solve real world applications.
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