Math 238 Differential Equations

Credit: 3 semester Hours

COURSE PREREQUISITES: MTH 227.

I. COURSE DESCRIPTION:

This course is an introduction to the basic theory of ordinary differential equations and applications of differential equation useful for students in the hard sciences, engineering and mathematics.

II . COURSE OBJECTIVES: As a result of successfully completing this course the student will be able to:

1. Analytically solve separable and linear first order ordinary differential equations;
2. Apply separable and linear first order ordinary differential equations to applied problems;
3. Demonstrate competence in the standard techniques of solving higher order ordinary
linear differential equations (undetermined coefficients, reduction of order and variation of parameters);
4. Understand the nature of solutions of ordinary linear differential equations;
5. Apply knowledge of ordinary linear differential equations to applied problems;
6. Solve higher order linear differential equations using linear differential operators;
7. Understand and apply the concepts of span, linear independence, basis and dimension;
8. Compute the Laplace transform of some standard functions;
9. Solve initial value problems by use of Laplace transforms;
10. Compute the matrix representation of a linear transformation;
11. Apply numerical techniques to solving ordinary differential equations;

III. CONTENT AND ORGANIZATION:

Chapters 1-3, 9, 14 in Simmons

IV. References:

I. Deferential Equations with Applications and Historical Notes, George F. Simmons, 2nd Ed., McGraw-Hill International Series in Pure and Applied Mathematics

2. A Short Course in Differential Equations, Rainville and Bedient, 4th Ed., MacMillan

V. Required (Graded) Assignments: 3- 100 pt tests, 1-200 point final, occasional quizzes.

VI. Evaluation Procedures: Grading System:

VII. TEXTBOOKS CURRENTLY BEING USED: Differential Equations with Applications and Historical Notes, George F. Simmons, 2nd Ed., McGraw-Hill International Series in Pure and Applied Mathematics

VIII. Other Important Information:

1. Attendance: Students with more than 1 week (2 classes) unexcused absences will be advised to dropped from the course.

2. If you have a disability that may prevent you from meeting the course requirements, contact the instructor before the end of the first week of classes to file a student disability request and to discuss a reasonable plan. Course requirements will not be waived but accommodations may be made to assist you in meeting the requirements, provided you are timely in working with the instructor to develop a reasonable accommodation plan.