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A clear, concise book that emphasizes finding solutions to differential equations where applications play an important role. Each chapter includes many illustrative examples to assist the reader. KEY TOPICS: The book emphasizes methods for finding solutions to differential equations. It provides many abundant exercises, applications, and solved examples with careful attention given to readability. Elementary Differential Equations includes a thorough treatment of power series techniques. In addition, the book presents a classical treatment of several physical problems to show how Fourier series become involved in the solution of those problems. The eighth edition of Elementary Differential Equations has been revised to include a new supplement in many chapters that provides suggestions and exercises for using a computer to assist in the understanding of the material in the chapter. It also now provides an introduction to the phase plane and to different types of phase portraits. MARKET: A valuable reference book for readers interested in exploring the technological and other applications of differential equations.
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.
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.
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