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	Functions	Elementary Algebra Basic understanding of Linear Equations Basic understanding of Solving Equations Basic understanding of Graphs	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	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 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 Polynomials Solving Quadratic Equations	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	Limits	Graphs Properties of Functions Domain Range Toolkit Functions	Define the limit of a function at a domain value. Find limits using graphs. Find limits numerically. Find limits using limit properties, including substitution.
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 Average Algebraic manipulations: - 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	Tangent Lines and Derivatives	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. 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 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	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	Review the inverse relation ship between exponential and logarithmic 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	Derivatives and Graphs	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 using the First Derivative Test. Use local extrema to solve real world problems.
Week 7	12.2	The Second Derivative	Closed Intervals Local Extrema	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	Optimization Applications	The First Derivative Test Second Derivative Test	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	Differentiation Rules 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. Solve real world problems using implicit differentiation.
Week 9	12.5	Related Rates	Solving Equations The Derivative as a Rate of Change Implicit Differentiation	Solve problems involving related rates in a variety of real world problems.
Week 11	13.1	Antiderivatives	Techniques for Finding Derivatives Derivative Properties Derivatives of Exponential Functions Derivatives of Logarithmic Functions	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	Integration by Substitution	Antiderivatives The Chain Rule	Find differentials of various functions. Find antiderivatives using integration by substitution. Solve simple initial value problems involving real world contexts.
Week 12	13.4	The Definite Integral	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	The Fundamental Theorem of Calculus	Antiderivatives The Definite Integral Integration by Substitution	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	Applications of Integrals	Solving Equations The Fundamental Theorem of Calculus Integration by Substitution	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	Differential Equations	Solving Equations Antiderivatives Integration by Substitution	Find general solutions to separable differential equations. Find particular solutions to separable differential equations. Solve real-world problems involving exponential growth and decay models.