# 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.

## Objectives

Throughout the course, these mathematical tools are applied to problems as varied as carbon dating, population growth, memory, criminology, and transportation planning.

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

• 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 outline

Course Units

• Unit 1: Functions, Graphs, and Models
• Unit 2: Limits and Differentiation
• Unit 3: Differentiation Techniques
• Unit 4: Applications of Differentiation
• Unit 5: Exponential and Logarithmic Functions
• Unit 6: Integration
• Unit 7: Integration Techniques and Applications

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
• 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

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. Dubriske, D. Student's solutions manual. 11th ed., (2016). For Bittinger, M. L., Ellenbogen, D. J., & Surgent, S. A. (2016). Calculus and its applications (11th ed.). Boston, MA: Pearson.
Type: ISBN-13: 978-0-321-99905-4

Good-quality scientific calculator is required.

## Assessments

In order to successfully complete this course, students must obtain at least 50% on the final mandatory examination and 50% overall.

 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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