MAT1133

Course Catalog

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

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
3.0	11.3	Rates of Change	Function Notation Graphs of Functions Equation of a Line Algebraic manipulations, e.g. 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. 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.
3.0	11.4	Tangent Lines and Derivatives	Function Notation Graphs of Functions Limits of Functions Weighted Average Function Evaluation Rates of Change Equation of a Line Algebraic manipulations, e.g. 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. 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.
3.0	11.4	The Derivative as a Function	Function Notation Graphs of Functions Limits of Functions Weighted Average Function Evaluation Average Rate of Change Equation of a Line Algebraic manipulations, e.g. 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. 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.

Topics List B

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.