STATE UNIVERSITY COLLEGE AT BUFFALO

Mathematics Department

Request for Course

I. Number and title of course:

Mathematics 316 - Intermediate Differential Equations

II. Reasons for Addition to the present Curricula:

A. This course is basic for applied mathematics offerings for mathematics and science majors.

B. This course is generally a prerequisite for other courses in applied mathematics and computer technology.

C. To provide an extension of Mathematics 315 Differential Equations) to other methods for solving Differential Equations.

D. This is one of the courses for the structure of the entire undergraduate program as recommended by the National committee on the undergraduate program in Mathematics.

E. This course is a replacement for Mathematics 415.

III. Major Objectives of the Course:

A. To illustrate the principles in solving physical

problems by mathematical methods.

B. To develop 'she understanding to confront scientific

situations with mathematical ideas.

C. To enable students to develop skills in the methods

of analyzing a physical problem.

IV. Behavioral Objectives:

The following represent a minimal 1ist of behavioral objectives. The student will be expected to solve each of the following types of problems.

A. To find Laplace transforms and Inverse replace transforms of elementary functions.

B. To solve initial value problems using Laplace transforms methods. To represent elementary functions in terms of Fourier Series.

D. To state and illustrate the principal theorems concerning Laplace transforms and Fourier Series.

E. To recognize and solve the Heat, Wave, and Laplace equations using the Separation of variables technique.

V. Topical Outline:

A. Laplace transforms

1. Notion of Laplace transform

2. Transforms of elementary functions

3. Transforming initial value problems

4. Transforms of derivatives

5. Derivatives of transforms

6. The Gamma function

B. Inverse Laplace transforms and applications

1. Notion of inverse transform

2. convolution theorem

3. Initial value problems

4. Applications to problems in vibrations, resonance and the simple pendulum.

C. Partial Differential Equations.

1. Notion of partial differential equation

2. Some partial differential equations of applied mathematics

3. Separation of variables

4. Conduction of heat in a slab

D. Fourier Series.

1. Orthogonality of a set of sines and cosines.

2. An expansion theorem

3. Numerical examples of Fourier Series.

4. Fourier sine and cosine series

E. Boundary value problems

1. line heat equation

2. The wave equation

3. Laplace equation

F. Transform methods

1. Power series and inverse transforms

2. The error function

3. Boundary value problems by transform methods

4. Diffusion problems by transform methods

VI. Bibliography, Texts and readings:

Churchill, R.V., Operational Mathematics 2nd Ed. New York; McGraw?Hill Book Company, 1956.

Greenspan, Donald, Introduction to Partial Differential Equations,New York;McGraw-Hill Book Company, l96l.

Hildebrand, Advanced Calculus for Applications, Englewood Cliffs, New Jersey, Prentice?Hall Inc., 1964.

Knopp, K., Infinite Sequences and Series, New York; Dover Publications Inc.,1956.

Lass, H., Elements of Pure and_applied Mathematics, New York; McGraw?Hill Book Co., 1957.

Rainville, Earl D., Special Functions, New York; The MacMillan Co., 1960.

Sagan, E., Boundary and Eigenvalue Problems in Mathematical Physics, New York; John Wiley and Sons, l96l.

Sokolinihoft, I.S., and R.M. Redheffer, Mathematics of Physics and Modern Engineering, New York, McGraw-Hill Book Co., 1958.

Weinberger, H.F., A First Course on Partial_Differential Equations, Waltham, Mass., Blasdell Publ. Co., 1905

Wylie, C.R. Advanced Engineering Mathematics, 3rd Ed., New York: McGraw?Hill Book co., 1965.

VII. Presentation and Evaluation:

A. Presentation by means of lectures, discussions, and individual projects.

B. Pretesting to determine the level of competency will provide for a maxi degree of individualization.

C. Evaluation by means of written exams, homework and class participation.

D. Each instructor?is individually responsible to publicly and explicitly state his methods of evaluation.

VIII. Prerequisites:

Mathematics 315
 
 

IX. Credit:

3 semester hours
 
 

X. Statement of Approval:
 
 

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

_________________(Date) Chairman:________________________

XI. Catalog Description:

Math 316 - Intermediate Differential Equations ?Laplace transform; inverse Laplace transform and applications, partial differential equations; Fourier series; Boundary value problems, transform methods applications. Prerequisites: Math 315.

XII. Statement of qualifications of faculty who will teach the course:

A Masters Degree in mathematics with special interest in the study of differential equations. A course similar to this one has been a part of our undergraduate program for five or six years. The following faculty have taught in this area during that time:

Robert C. Frascatore, Assistant Professor of Mathematics M.A. University of Maine (1961)

Edward Newberger, Assistant Professor of Mathematics Ph.D. Indiana University (1959)

Ki-Choul Our, Professor of Mathematics Ph.D. Syracuse University (1967)