CALCULUS FOR TEACHERS 2

MATH 615

Course Description

This course provides an intermediate level knowledge of mathematical concepts, techniques, and applications related to calculus and their application to the arts and sciences, professional studies and education.

Prerequisite: MATH 614 Calculus for Teachers I

Goals of the Course

1. To provide a suitable approach to calculus for teachers in both elementary and secondary schools.

2. To explore potential techniques for teaching selected concepts of calculus.

3. To investigate connections between calculus and other subjects, such as arts and sciences and allied branches of mathematics.

Evaluation Measures

1. Participation in classroom activities

2. Preparation of assignments

3. Written examinations

Course Contents

I Integration

1 Introduction

2 The indefinite integral

3 Applications of indefinite integration

4 Brief review of trigonometry

5 Differentiation and integration of sines and cosines

6 Area under a curve

7 Computation of areas as limits

8 Areas by calculation

9 The definite integral and the Fundamental Theorem of integral calculus

10 The trapezoidal rule for approximating an integral

11 Some comments on notation

12 Summary

Miscellaneous problems

II. Applications of the Definite Integral

1 Introduction

2 Area between two curves

3 Distance

4 Volumes

5 Approximations

6 Length of a plane curve

7 Area of a surface of revolution

8 Average value of a function

9 Moments and center of mass

10 Centroid and center of gravity

11 The Theorems of Pappus

12 Hydrostatic pressure

13 Work

Miscellaneous problems

III Transcendental Functions

1 The trigonometric functions

2 The inverse trigonometric functions

3 Derivatives of the inverse trigonometric functions

4 The natural logarithm

5 The derivative of ln x

6 Properties of natural logarithms

7 Graph of y = ln x

8 The exponential function

9 The function a^u

10 The function log u

11 Differential equations

Miscellaneous problems

Bibliography

Anton, Howard, Calculus, a new horizon, 6^th Ed., John Wiley & Sons, New York, N.Y., 1999.

Berkeley, Dennis, Applied Calculus. Philadelphia, Pa.: Saunders, 1990.

Bittinger, Marvin, Calculus and its applications, 7^th Ed., Addison-Wesley, Reading Mass., 2000.

Coughlin/Zitarelli, Brief Calculus with Applications, Saunders Pub., Philadelphia, Pa., 1990.

Demana, Franklin. 1998. Graphing Calculator and Computer Graphing Laboratory Manual, 2^nd ed. New York: Addison-Wesley Publishing Company.

Geckmann, Charlene, Exploring Calculus with a Graphing Calculator. Reading, Mass. Addison-Wesley, 1992.

Harris, Kent, Discovering Calculus with Maple, New York, Wiley, 1992.

Hughes-Hallett, Deborah, and Andrew Gleason, Calculus: Single Variable. New York: John Wiley, 1997.

Kaplan, Wilfred, Advanced Calculus. Cambridge, Mass,: Addison Wesley, 1991.

Larson, Roland E., Robert P. Hostetler, and Bruce Edwards. 1998. Calculus with Analytic Geometry, 6^th ed. Boston: Houghton Mifflin Company.

Simmons, George, Calculus Gems. New York: McGraw-Hill, 1992.

Strang, Gilbert, Calculus. Wellesley, Mass: Wellesley-Cambridge, 1991.

Stewart, James, Calculus with early transcendental functions, 4^th Ed., Brooks/Cole, Pacific Grove Ca., 1999.

Thomas, George and Finney, Ross, Calculus and Analytical Geometry. Reading, Mass. Addison Wesley, 1992.

Addenda to Bibliography

Mathematical Association of America, Resources for Calculus Collection. Washington, DC, 1993.

Vol 1: Learning by Discovery: A Lab Manual for Calculus

Vol 2: Calculus Problems for a New Century

Vol 3: Applications of Calculus

Vol 4: Readings for Calculus

Periodicals

The Mathematics Teacher

The American Mathematics Monthly

School Science and Mathematics