Elementary Differential Equations

by Rainville, Earl D.; Bedient, Phillip E.

• ISBN13: 9780023978609
• ISBN10: 0023978600
• Format: Hardcover
• Copyright: 1989-01-01
• Publisher: Macmillan Coll Div

Summary

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. 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. A valuable reference book for readers interested in exploring the technological and other applications of differential equations.

Table of Contents

Definitions; Families of Curves

Equations of Order One

Numerical Methods

Elementary Applications

Additional Topics on Equations of Order One

Linear Differential Equations

Linear Equations with Constant Coefficients

Nonhomogeneous Equations: Undetermined Coefficients

Variation of Parameters

Applications

Linear Systems of Equations

Nonhomogeneous Systems of Equations

The Existence and Uniqueness of Solutions

The Laplace Transform

Inverse Transforms

Nonlinear Equations

Power Series Solutions

Solutions Near Regular Singular Points

Equations of Hypergeometric Type

Partial Differential Equations

Orthogonal Sets of Functions

Fourier Series

Boundary Value Problems

Additional Properties of the Laplace Transform

Partial Differential Equations Transform Methods

Answers to Odd-numbered Exercises

Index

Table of Contents provided by Publisher. All Rights Reserved.