# 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 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

Please note that weeks 5, 10, and 14 are used for review and examination.

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
• 3.1
• Identify and use Function notation.
• Determine whether a table or equation defines a function.
• Find the domain of a function (including piecewise defined functions).
• Evaluate Functions (including piecewise defined 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
• Convert quadratic functions between the general and standard (vertex) forms.
• 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, including minimization, maximization, equilibrium, and break-even analysis.
Week 2
• 11.1
• Identify and use limit notation.
• Find limits of functions at both domain and non-domain values.
• Find limits using graphs.
• Find limits numerically.
• Find limits using limit properties, including substitution.
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
• Describe the average rate of change of a function in terms of its algebraic and geometric meanings.
• Calculate average rates of change for various functions.
• Find instantaneous rates of change of linear and quadratic functions using the limit definition.
• Solve real-world problems involving average and instantaneous rates of change.
• Describe the instantaneous rate of change of a function and its relationship to average rate 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.
• Calculate 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 limit 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
• Identify that the power rule is based upon the limit definition of the derivative.
• Find derivatives using the constant rule, power rule, constant multiple 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
• Review the inverse relationship between exponential and 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
• 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 using the First Derivative Test.
• Use local extrema to solve real world problems.
Week 7
• 12.2
• Define notation for higher derivatives.
• Find the second derivative and higher-order derivatives of a function.
• Describe acceleration using the second derivative.
• Identify the intervals on which a function is concave up and concave down.
• Find the points of inflection of a function.
• Find the local extrema of a function using the Second Derivative Test.
• 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
• Find derivatives of implicit functions.
• Find lines tangent to graphs of implicit functions.
• Solve real world problems using implicit differentiation.
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.
• Use anti-differentiation to solve simple initial-value problems involving real world contexts.
Week 11
• 13.2
• Find differentials of various functions.
• Find antiderivatives using integration by substitution.
• Use anti-differentiation to solve simple initial-value problems involving real world contexts.
Week 12
• 13.4
• Graphs of functions
• Areas of quadrilaterals and triangles.
• 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 calculate definite integrals.
• Calculate 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
• 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.