William F. Trench

• Elementary Differential Equations consists of ten chapters and 654 pages.
• Elementary Differential Equations with Boundary Value Problems has an additional three chapters and a total of 797 pages.
• Originally published by Brooks Cole/Thomson Learning
• Student manual available with solutions for even numbered problems
• Instructor’s manual available to verified faculty
• May be printed and distributed with a nominal charge to cover costs
• For more information and to download:
  Elementary Differential Equations
  Elementary Differential Equations with Boundary Value Problems
  Student Solution Manual

These texts are appropriate for a first course in differential equations for one or two semesters. There are more than 2000 exercises, and the student manual has solutions for most of the even numbered ones.

From the preface:

Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 414 exercises – identified by the symbols C  and  CG – that call for graphics or computation and graphics. There are also 79 laboratory exercises – identified by L  – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.

Table of Contents

1. Introduction
2. First Order Equations
3. Numerical Methods
4. Applications of First Order Equations
5. Linear Second Order Equations
6. Applcations of Linear Second Order Equations
7. Series Solutions of Linear Second Order Equations
8. Laplace Transforms
9. Linear Higher Order Equations
10. Linear Systems of Differential Equations
11. Boundary Value Problems and Fourier Expansions
12. Fourier Solutions of Partial Differential Equations
13. Boundary Value Problems for Second Order Linear Equations

The author welcomes corrections and updates the books regularly. The most recent versions are dated July 2013.