STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Revised Course Proposal

I. Number and title of course

Mathematics 263 - Calculus III
II. Reasons for addition to the 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 the calculus of several variables and infinite series and their important applications through algorithmic techniques and/or computer usage.
IV. Topical outline
A. Vectors
1. Vectors in plane; vectors in space
2. Dot Product; Cross Product
B. Partial Differentiation
1. Functions of several variables
2. Limits and continuity
3. Partial Derivatives
a. Interpretation of partial derivatives
b. Higher order partials
4. Directional derivatives and the gradient
5. The chain rule
6. Maxima and minima
C. Multiple Integrals
1. Double integrals
2. Iterated integrals
3. Polar coordinates
4. Triple integrals
5. Cylindrical and spherical coordinates
6. Applications of double and triple integrals
a. Area
b. Volume
c. Surface area.
 D. Infinite Surfaces
1. Sequences

2. Infinite series

3. Tests for convergence and divergence

a. Nth term test, comparison test
b. Integral test, the p?series
c. Root test, Ratio test
4. Alternating series; Absolute convergence

5. Power series

6. Taylor series

a. Taylor formula with remainder
b. Taylor series theorem
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, 1981.
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 w th 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 162

Co:requisite: MAT 264

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 ______________(Date)      ________________________ (Dept. Chairman)
X.Catalog Description
MATH 263-Calculus III: Vectors, partial differentiation, multiple integrals, and infinite series. 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.