Differential Equations (Textbooks in Mathematics)

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This book illustrates how MAPLE can be used to supplement a standard, elementary text in ordinary and partial differential equation. MAPLE is used with several purposes in mind.

The authors are firm believers in the teaching of mathematics as an experimental science where the student does numerous calculations and then synthesizes these experiments into a general theory.

Projects based on the concept of writing generic programs test a student's understanding of the theoretical material of the course. A student who can solve a general problem certainly can solve a specialized problem. The authors show MAPLE has a built-in program for doing these problems. While it is important for the student to learn MAPLEŚ in built programs, using these alone removes the student from the conceptual nature of differential equations.

The goal of the book is to teach the students enough about the computer algebra system MAPLE so that it can be used in an investigative way. The investigative materials which are present in the book are done in desk calculator mode DCM, that is the calculations are in the order command line followed by output line. Frequently, this approach eventually leads to a program or procedure in MAPLE designated by proc and completed by end proc.

This book was developed through ten years of instruction in the differential equations course.

Table of Contents

1. Introduction to the Maple DEtools

2. First-order Differential Equations

3. Numerical Methods for First Order Equations

4. The Theory of Second Order Differential Equations with Con-

5. Applications of Second Order Linear Equations

6. Two-Point Boundary Value Problems, Catalytic Reactors and

7. Eigenvalue Problems

8. Power Series Methods for Solving Differential Equations

9. Nonlinear Autonomous Systems

10. Integral Transforms