# MATH 1157: Calculus for Biological and Social Sciences

This course emphasizes applications rather than theory. Students begin with a review of algebra, to ensure the necessary mathematical skills to succeed in the course, and before they are introduced to limits and continuity. Students then progress to differential and integral calculus for polynomial, exponential and logarithmic functions and their applications to curve sketching, maxima, and minima. Students apply these mathematical tools to a variety of 'real-world' problems, including medical issues, epidemics, carbon dating, memory and criminology.

## 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 the biological and social sciences.
• Use the theory of maxima and minima to find optimal solutions to problems in the biological and social 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.
• Determine whether an improper integral converges or diverges, and if it converges, find its value.

## Course topics

• Limits and continuity, average rate of change, differentiation using limits
• Sum-Difference Rule, Power Rule, rates of change, Product and Quotient Rules, Extended Power Rule, Chain Rule, higher-order derivatives
• The shape of a graph, derivatives and graph sketching, maxima and minima with applications, differentials, implicit differentiation
• Exponential and logarithmic functions, natural logarithmic function, applications to biology, anthropology, psychology, and sociology
• Antiderivative, area, fundamental theorem of calculus, definite integral
• Area between curves, integration techniques (substitution and parts), application of integrals, improper integrals

## Required text and materials

The following materials are required for this course:

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.

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 final mandatory 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 Functions 12% Assignment 4: Applications of Differentiation 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.

Search To Top