# 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.

## Learning outcomes

• Compute the 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.
• Find the area under a curve and the area of the region enclosed by two graphs in determining the consumer surplus and producer surplus.
• Infer whether an improper integral converges or diverges and, if it converges, find its value.

## Course topics

• Exponents, equations, inequalities, interval notations, graphs, functions, compound interest
• Limits and continuity, average rate of change, differentiation using limits
• Sum-difference rule, power rule, rates of change, marginal cost, marginal revenue, marginal profit, product and quotient rules, chain rule, higher-order derivatives
• Shape of a graph, derivatives and graph sketching, maxima and minima with applications, minimizing inventory costs, differentials, implicit differentiation, related rates
• Exponential and logarithmic functions, natural logarithmic function, uninhibited growth model, models of limited growth, depreciation
• Antiderivative, area, the fundamental theorem of calculus, definite integral
• Area between curves, integration techniques (substitution and parts), consumer and producer surplus, the amount of an annuity, present value, improper integrals

## Required text and materials

The following textbooks are required for this course, students will receive the following:

1. Bittinger, M. L., Ellenbogen, D. J., & Surgent, S. A. (2019). Calculus and its applications plus MyLab Math with Pearson eText (12th ed.). Boston, MA: Pearson.
Type: Textbook: ISBN-13: 9780135308035
1. Dubriske, D. (2019). Student’s solutions manual (12th ed.). For Bittinger, M. L., Ellenbogen, D. J., & Surgent, S. A. (2019). Calculus and its applications (12th ed.). Boston, MA: Pearson.
Type: Textbook. ISBN-13: 9780135165683

A good-quality scientific calculator with scientific notation and logarithmic, exponential, and trigonometric functions (including inverse functions) is required for student coursework.
Note: Only a scientific calculator will be allowed for the final exam.

## Assessments

Please be aware that should your course have a final exam, you are responsible for the fee to the online proctoring service, ProctorU, or to the in-person approved Testing Centre. Please contact exams@tru.ca with any questions about this.

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.

Note: The final exam for this course is only available as a paper exam and must be taken in person at an approved Testing Centre. Please email exams@tru.ca with any questions.

 Assignment 1: Limits and Differentiation 12% Assignment 2: Differentiation Techniques 12% Assignment 3: Exponential and Logarithmic 12% Assignment 4: Applications of Differentation 12% Assignment 5: Integration Techniques and Applications 12% Final Exam (mandatory) 40% Total 100%

## Open Learning Faculty Member Information

An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of the course.

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