I. Catalog Description

MATH 115 Applied Mathematics for Business 4 credits

4 lecture hours

(4c-0l-4sh)

Prerequisites: MATH 105 or MATH 110 or equivalent high school preparation.

Note: A student may not take MATH 115 after successfully completing a calculus course without the written approval of the mathematics department chairperson.

After a review of elementary functions (including logarithmic and exponential functions), introduces business majors to mathematics of finance and central ideas of the calculus (limit, derivative, and integral). Emphasis on applications to business and economics.

II. Course Objectives

1. Students will understand and take advantage of pattern recognition in the study of mathematics.

2. Students will make a careful study of functions and their application to business and economics.

3. Students will make a careful study of the mathematics of finance.

4. Students will understand how to interpret functions expressed analytically and graphically.

5. Students will understand the limit process and how it pertains to functions in business and economics.

6. Students will be able to calculate the derivative of a function and interpret its meaning.

7. Students will be able to calculate the integral of a function and interpret its meaning.

8. Students will leave the course with a solid set of skills and a conceptual framework to equip the students for the future study of business and economics.

III. Course Outline

A. Library of Functions (10 hours)

1. Functions

2. Linear Functions

3. Quadratic Functions

4. Polynomial Functions

5. Rational Functions

6. Exponential Functions

7. Logarithmic Functions

B. Mathematics of Finance (6 hours)

1. Simple Interest

2. Compound Interest

3. Future Value of an Annuity

4. Present Value of an Annuity

C. The Derivative (11 hours)

1. Rates of Change

2. Limits

3. The Derivative

4. Power Rules and Summation Rules

5. Product and Quotient Rule

6. Chain Rule: Power Form

7. Marginal Analysis in Business and Economics

D. Graphing and Optimization (8 hours)

1. Continuity and Graphs

2. First Derivative and Graphs

3. Second Derivative and Graphs

4. Other Curve Sketching Techniques

5. Optimization: Absolute Maxima and Minima

E. Additional Topics in Differentiation (5 hours)

1. The Constant e and Continuous Compound Interest

2. Derivatives of Exponential and Logarithmic Functions

3. Chain Rule: General Form

F. Integration (8 hours)

1. Antiderivatives and Indefinite Integrals

2. Integration by Substitution

3. Introduction to the Definite Integral

4. The Fundamental Theorem of Calculus

5. Applications of the Integral to Business and Economics

The remaining eight hours are for four review classes and four tests.

IV. Evaluation Methods

See your instructor’s syllabus

V. Required Textbook

Barnett, Raymond, Michael Ziegler, and Karl Byleen. Applied Mathematics for Business, Economics, Life Sciences, and Social Sciences. Upper Saddle River, NJ: Prentice-Hall, Inc., 2000. (Subject to change)

VI. Special Resource Requirements

Some instructors may require students to purchase a graphing calculator.

VII. Bibliography

Committee on the Mathematical Sciences in the Year 2000. Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Washington, DC : National Academy Press, 1989.

Haeussler, Ernest, and Richard Paul. Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences. Upper Saddle River, NJ: Prentice-Hall, Inc., 1999.

Hughes-Hallet, Deborah, et al. Applied Calculus. New York: John Wiley & Sons, Inc., 1999.