Difference between revisions of "MAT1133"

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* Find differentials of various functions.
 
* Find differentials of various functions.
 
* Find antiderivatives using integration by substitution.
 
* Find antiderivatives using integration by substitution.
* Solve initial value problems involving real world contexts.
+
* Solve simple initial value problems involving real world contexts.
 
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|Week 12
 
|Week 12

Revision as of 16:08, 15 December 2020

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 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

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
  • 3.1
  • 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
  • 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
  • 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
  • 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
  • Find limits using graphs.
  • Find limits numerically.
  • Use limit properties to find limits.
Week 2
  • 11.2
  • 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
- 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • The derivative as a rate of change, substitution, general problem reading/solving skills.
  • Find derivatives of implicit functions.
  • Find lines tangent to graphs of implicit functions.
Week 9
  • 12.5
  • Solve problems involving related rates in a variety of real world problems.
Week 11
  • 13.1
  • Find antiderivatives of functions using the power, constant-multiple, and sum-or-difference differentiation rules, as well as derivatives of exponential and logarithmic functions.
  • Solve simple initial value problems involving real world contexts.
Week 11
  • 13.2
  • Find differentials of various functions.
  • Find antiderivatives using integration by substitution.
  • Solve simple initial value problems involving real world contexts.
Week 12
  • 13.4
  • Graphs of functions
  • Areas of rectangles, triangles, and trapezoids.
  • Use numerical integration technology to calculate definite integrals.
  • Apply understanding of definite integrals to solve real world problems.
Week 12
  • 13.5
  • Apply the fundamental theorem of calculus to find definite integrals.
  • Find the area between the graph of a non-negative function and the x-axis on a closed interval.
  • Apply understanding of definite integrals to solve real world problems.
Week 13
  • 13.6
  • Find the area between the graph of a function and the x-axis on a closed interval.
  • Find the area between the graphs of two functions.
  • Apply understanding of definite integrals to solve real world problems, including consumers’ surplus and producers’ surplus.
Week 15
  • 13.7
  • Find general solutions to separable differential equations.
  • Find particular solutions to separable differential equations.
  • Solve real-world problems involving exponential growth and decay models.