STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Revised Course Proposal

I. Number and title of course

Mathematics 162 - Calculus II

II. Reasons for addition to present curricula (presently offered) Basic course necessary for all students in the areas of mathematics and most sciences because of its many important concepts, applications, and computational methods.

III. Major objectives of the course To acquaint the student with many concepts of integral calculus and their important applications through algorithmic techniques and/or computer usage.

IV. Topical Outline

A. The Definite Integral

1. Riemann sums

2. Numerical integration

a. Trapezoidal Rule
b. Simpson's Rule 3. Fundamental theorem of calculus B. Applications of the Definite Integral 1. Area of a region in the plane

2. Volume of a solid of revolution

3. Arc length

 C. Logarithmic and Exponential Functions 1. Differentiation and integration formulas

2. Applications

 D. Inverse Trigonometric Functions (optional)

E. Techniques of Integration

1. Integration by parts

2. Substitution techniques

3. Use of tables (optional)

4. Partial fractions (optional)

5. Improper integrals


V. Bibliography

Apostol, T.M. Calculus Vols. I, II, Blaisdell Pub. Co., Massachusetts, 1967.

Courant, R. and John, F. Calculus and Analysis, Interscience Publishers, New York, 1965.

Ellis, R. and Gulick, D. Calculus with Analytic Geometry, Harcourt Brace Jovanovich, Inc., 1982.

Gillman, L. and McDowell, R.H. Calculus, W.W. Norton and Co., New York, 1978.

Grossman, S.I. Calculus, Academic Press, ]L981. Supplement: Computing for Calculus by Christensen, M.

Kline, M. Calculus, An Intuitive and Physical Approach, John Wiley & Sons, New York, 1977.

Purcell, E.J. Calculus with Analytic Geometry, Prentice-Hall, Inc., New Jersey, 1978.

Simon, A.B. Calculus with Analytic Geometry, Scott, Foresman ~ Co., Illinois 1982.

Stein, S.K. Calculus and Analytic Geometry, McGraw-Hill, New York, 1982.

Thomas, G.B. Calculus and Analytic Geometry, Addison-Wesley Pub. Co., 1980.

 VI. Presentation and evaluation

Lectures, class discussions, assigned) problems, written examinations.

VII. Prerequisite

MAT 161

Co-requisite: MAT 164

VIII. Credit

Three semester hours

IX. Statement of approval

This revised course proposal was examined in accord with recommended procedures and has been approved by the Mathematics Department on

Dept. Chairpersons

X. Catalog Description MATH 162-CALCULUS II:

The definite integral, the fundamental theorem of calculus, applications of the definite integral, techniques of integration logarithmic and exponential functions. Applications studied through algorithmic techniques and/or computer usage.

XI. Statement of qualifications of faculty who will teach the course

All members of the Department of Mathematics

XII. Support services required

Present classroom facilities and Academic computing services are adequate.