# MATH 1171: Calculus for Business and Management Sciences

This introductory course emphasizes the application of differential and integral calculus to the problems encountered in business and management science. The course begins with a brief review of algebra in order to ensure that students have the necessary mathematical skills to succeed in the course. This review is followed by an introduction to limits and continuity; students then study differential and integral calculus for polynomial, exponential and logarithmic functions and their applications to curve sketching, maxima, and minima.

## Objectives

After successfully completing this course, students will be able to:

• Compute first and second derivatives of a large class of functions and apply differentiation techniques to the solution of simple problems in business and management sciences.
• Use the theory of maxima and minima to find optimal solutions to problems in business and management sciences.
• Use the properties of exponential and logarithmic functions to solve applied problems.
• Find the indefinite and definite integrals for a variety of functions and find the area under a curve and between two "reasonable" curves.
• Infer whether an improper integral converges or diverges. If it converges, compute its value.

## Course outline

Unit 1: Functions, Graphs, and Models: Exponents, equations, inequalities, interval notations, graphs, functions, compound interest

Unit 2: Limits and Differentiation: Limits and continuity, average rate of change, differentiation using limits

Unit 3: Differentiation Techniques: Sum-difference rule, power rule, rates of change, marginal cost, marginal revenue, marginal profit, product and quotient rules, chain rule, higher-order derivatives

Unit 4: Applications of Differentiation: Shape of a graph, derivatives and graph sketching, maxima and minima with applications, minimizing inventory costs, differentials, implicit differentiation, related rates

Unit 5: Exponential and Logarithmic Functions: Exponential and logarithmic functions, natural logarithmic function, uninhibited growth model, models of limited growth, depreciation, restoration of market equilibrium price

Unit 6: Integration: Anti derivative, area, fundamental theorem of calculus, definite integral

Unit 7: Integration Techniques and Applications: Area between curves, integration techniques (substitution and parts), consumers' and producers' surplus, the amount of an annuity, present value, improper integrals

## Required text and materials

1. Bittinger, M. L., Ellenbogen, D. J., & Surgent, S. A. Calculus and its Applications. (11th ed.). Boston, MA: Pearson, (2016).
Type: ISBN-13: 978-0-321-97939-1
1. Dubriski, D. Student's Solutions Manual . (11th ed.). (2016).
Type: ISBN-13: 978-0-321-99905-4

A good-quality scientific calculator with scientific notation and logarithmic, exponential, and trigonometric functions (including inverse functions) is required for student coursework. A graphing calculator is not allowed.

## Assessments

To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course and 50% or higher on the mandatory final exam.

 Assignment 1: Limits and Differentiation 8% Assignment 2: Differentiation Techniques 8% Assignment 3: Applications of Differentiation 8% Assignment 4: Exponential and Logarithmic Functions 8% Assignment 5: Integration Techniques and Applications 8% Final Exam * 60% Total 100%

* Mandatory

## Open Learning Faculty Member

An Open Learning Faculty Member is available to assist students. Primary communication is through the Learning Environment's "Mail" tool or by phone. Students will receive the necessary contact information at start of course.

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