DIFFERENTIAL EQUATIONS

MA 310

Catalogue Description

This is the first course in differential equations, including such topics as separate variables, homogeneous equations, integrating factors, linear and higher order differential equations, and applications. 3 credits. Prerequisite: Ma 290 Calculus III or equivalent.

Goals

A. To serve as an introduction to differential equations.

B. To utilize a student's background in Calculus in solving differential equations.

C. To illustrate several of the many applications of differential equations.

Procedures

A. Lecture/Discussion

B. Readings and assigned problems

Course Content

A. Introduction

1. Classification of Differential Equations

2. History

B. First Order Differential Equations

1. Linear Equations

1. Separable Equations

2. Exact Equations

3. Non Exact Equations and Integrating Factors

4. Homogeneous Equations

2. Existence and Uniqueness Theorem

3. Applications of First Order Linear Equations

C. Second Order Linear Equations

1. Introduction

2. Fundamental Solutions of the Homogeneous Equation

3. Linear Independence

4. Reduction of Order

5. Homogeneous Equations with Constant Coefficients

6. Nonhomogeneous Equations

A. Method of Undetermined Coefficients

B. Method of Variation of Parameters

D. Higher Order Linear Equations

1. Introduction

2. General Theory of nth Order Linear Equations

3. Homogeneous Equations with Constant Coefficients

4. Method of Undetermined Coefficients

5. Method of Variation of Parameters

Evaluation Methods

1. (2) - In-House Exams - 40%

2. (1) - Take Home Exam - 15%

3. (5) - Quizzes - 15%

4. Final Exam - 30%

Bibliography

Required Text: Zill, Dennis G., A First Course in Differential Equations, 5th Ed., PWS-Kent, Boston, Mass., 1993.

Boyce, William E., and DiPrima, Richard C., Elementary Differential Equations and Boundary Value Problems, 4th Ed., John Wiley & Sons, New York, 1986. *

Braun, M., Differential Equations and Their Applications, 3rd Ed., Springer-Verlag, New York, 1986.

Coddington, E.A., An Introduction to Ordinary Differential Equations, Prentice Hall, Emglewoood Cliffs, N.J., 1961.

Guterman, Martin M, and Nitecki, Zbigniew H., Differential Equations, A First Course, 2nd Ed., Saunders Publishing, N.Y., 1988.

Haines, Charles W., Solutions Manual to Accompany Elementary Differential Equations and Boundary Value Problems by William Boyce and Richard C. DiPrima, John Wiley & Sons, N.Y., 1986.

Ince, E.L., Ordinary Differential Equations, London: Longmans, Green, 1927, New York: Dover, 1956. *

Nagle, R. Kent and Saff, Edward B., Fundamentals of Differential Equations, 2nd Ed., Benjamin Cummings Co., N.Y. 1989.

Rainville, Earl D. and Bedient, Phillip E., Elementary Differential Equations, 7th Ed., MacMillan Publishing Co., 1989.

Simmons, G.F., Differential Equations with Applications and Historical Notes, McGraw Hill, New York, 1972. *

Software

Phase Portraits by Herman Gollwitzer, MacIntosh, available from Kinko's Academic Courseware Exchange.

DE Graph by Henry C. Pinkham, MacIntosh, available from Kinko's Academic Courseware Exchange.

Phaser by Huseyin Kocak, Springer-Verlag, New York, N.Y., 1989.

* means in New Jersey City University Library