Elementary Differential Equations

Elementary Differential Equations, 8/e

Earl D. Rainville, Deceased, University of Michigan
Phillip E. Bedient, Franklin & Marshall College
Richard E. Bedient, Hamilton College

Published October, 1996 by Prentice Hall Engineering/Science/Mathematics

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Differential Equations-Mathematics

Summary

This clear, concise fairly easy classic text is particularly well-suited to courses that emphasize finding solutions to differential equations where applications play an important role. Many illustrative examples in each chapter help the student to understand the subject. Computer applications new to this edition.

Features

This, classic ODE book, has been so successful because it is the clearest and easiest of all texts in this market.
This is the shortest of all the major ODE texts (it covers boundary values problems and PDEs. The brevity makes it usable in quarter schools.
Includes abundant exercises and applications.
Presents a thorough treatment of power series techniques.
Presents a classical treatment of select physical problems to show how Fourier series are utilized in the solution of these problems.
NEW—Most chapters include a new section with suggestions and exercises for using a computer to assist in the understanding of the material in the chapter.
NEW—Provides an introduction to the phase plane and to different types of phase portraits.

Table of Contents

1. Definitions; Families of Curves.
2. Equations of Order One.
3. Numerical Methods.
4. Elementary Applications.
5. Additional Topics on Equations of Order One.
6. Linear Differential Equations.
7. Linear Equations with Constant Coefficients.
8. Nonhomogeneous Equations: Undetermined Coefficients.
9. Variation of Parameters.
10. Applications.
11. Linear Systems of Equations.
12. Nonhomogeneous Systems of Equations.
13. The Existence and Uniqueness of Solutions.
14. The Laplace Transform.
15. Inverse Transforms.
16. Nonlinear Equations.
17. Power Series Solutions.
18. Solutions Near Regular Singular Points.
19. Equations of Hypergeometric Type.
20. Partial Differential Equations.
21. Orthogonal Sets of Functions.
22. Fourier Series.
23. Boundary Value Problems.
24. Additional Properties of the Laplace Transform.
25. Partial Differential Equations Transform Methods.
Answers to Odd-numbered Exercises.
Index.