STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Course Revision

I. Number and Title of Course

Mathematics 315 - Differential Equations

II. Reasons for Addition to the Present Curricula

This is not a new course but an updating of a current course
 

III. Major Objectives of the Course

A. To acquaint the student with methods of solution of various types of differential equations.

B. To familiarize the student with some applications of differential equations to other areas such as physics, chemistry, and biology.

C. To give, wherever possible, the theoretical foundations for the methods of A.
 
 

 IV. Topical Outline

A. Brief introduction

1. Definition of differential equation and a solution

2. Types of differential equations

a. Ordinary, partial

b. Order, degree

3. Origin of differential equations

B. First Order Equations

1. Linear

a. Variable separable

b. General method of solution with integrating factor

2. Nonlinear

a. Graphical method of integral curves

b. Variables separable

c. Exact equations

d. Integrating factors

e. Homogeneous equations

 3. Applications

1. Decay problems, orthogonal trajectories, mechanics, etc.
 

 C. Second Order Linear Equations

 1. Fundamental solutions of homogeneous equations

a. Wronskian

b. Superposition principle

c. Differential operator

d. Linear independence

e. Reduction of order

f. Homogeneous equations with constant coefficients

i. Real roots

ii. Complex roots

2.Nonhomogeneous equations

a. Undetermined coefficients

b. Variation of parameters

3. Applications

a. Vibrations, electrical networks

4. Series solutions

a. Near ordinary points

b. Near singular points

D. Systems of First Order Equations

1. Brief introduction methods of solution of linear systems

2. Basic theory of linear systems

3. Linear homogeneous system with constant coefficients

a. Use of Wronskian

b. Complex and repeated roots

4. Linear nonhomogeneous systems

 E. Higher Order Linear Equations

1. Homogeneous equation with constant coefficients

2. Undetermined coefficients

3. Variation of parameters

 V. Bibliography, Texts, and Readings

 Edwards, C.H., and Perry, D.E., Elementary Differential Equations with Applications, Englewood Cliffs, NJ, Prentice Hall, 1985.

Guterman, M., and Nitecki, F., Differential Equations, New York, NY, Saunders, 1984.

Iwaardan, John, Ordinary Differential Equations with Numerical Techniques, New York, NY, Harcourt, Brace, Jovanovich, 1985.

Nagle, R.K., and Saff, E.B., Fundamentals of Differential Equations, Menlo Park, CA, Benjamin Cummings Publishing Co., 1986.

Powers, D.L.,Elementary Differential Equations with Boundary Value Problems, Boston, MA, Prindle Weber, and Schmidt, 1985.

Rainville, E., and Bedient, P.E., Elementary Differential Equations New York, NY, Macmillan, 1981.

Spiegle, M., Applied Differential Equations, Englewood Cliffs, NJ, Prentice Hall, 1981.

Tierney, John,Differential Equations, Boston, MA, Allyn and Bacon, 1985.

VI. Presentation and Evaluation

The lecture-discussion method of presentation is used Evaluation will be based on examinations, and/or assigned problems.

VII. Prerequisites

MAT 263 or permission from instructor

VIII. Credit

Three semester hours

IX. Statement of Approval

 This course updating proposal was examined in accord with established procedures and was approved by the Department of Mathematics on May 5, 1986.

 ______________________________ (Department Chairperson)

X. Catalog Description

315-DIFFERENTIAL EQUATIONS. Preliminary ideas on order, degree, and solutions, formation of differential?equations, differential equations of first order, linear equations with constant coefficients, special high order equations, simultaneous equations, linear equations of the second order, series solutions.

XI. Statement of qualifications of faculty who will teach course All faculty who have completed one years study beyond the Master's degree.
 
 

XII. Support Services Required: Present classroom facilities are adequate.