The Fourth Edition of the best-selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. Includes new material on matrix methods, numerical methods, the Laplace transform, and an appendix on polynomial equations. Stresses fundamental methods, and features traditional applications and brief introductions to the underlying theory.

Differential Equations and Their Solutions.

First-Order Equations for Which Exact Solutions Are Obtainable.

Applications of First-Order Equations.

Explicit Methods of Solving Higher-Order Linear Differential Equations.

Applications of Second-Order Linear Differential Equations with Constant Coefficients.

Series Solutions of Linear Differential Equations.

Systems of Linear Differential Equations.

Approximate Methods of Solving First-Order Equations.

The Laplace Transform.

Appendices
Suggested Reading
Answers to Odd-Numbered Exercises
Index