Elementary Differential Equations and Boundary Value Problems, 9th Edition

by William E. Boyce (Rensselaer Polytechnic Institute); Richard C. DiPrima

• ISBN13: 9780470383346
• ISBN10: 0470383348
• Edition: 9th
• Format: Hardcover
• Copyright: 2008-10-01
• Publisher: Wiley

Summary

Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.

Table of Contents

Preface

Introduction 1

Some Basic Mathematical Models

Direction Fields

Solutions of Some Differential Equations

Classification of Differential Equations

Historical Remarks

First Order Differential Equations

Linear Equations

Method of Integrating Factors

Separable Equations

Modeling with First Order Equations

Differences Between Linear and Nonlinear Equations

Autonomous Equations and Population Dynamics

Exact Equations and Integrating Factors

Numerical Approximations: Euler's Method

The Existence and Uniqueness Theorem

First Order Difference Equations

Second Order Linear Equations 135

Homogeneous Equations with Constant Coef?cients

Fundamental Solutions of Linear Homogeneous Equations

The Wronskian

Complex Roots of the Characteristic Equation

Repeated Roots

Reduction of Order

Nonhomogeneous Equations

Method of Undetermined Coefficients

Variation of Parameters

Mechanical and Electrical Vibrations

Forced Vibrations

Higher Order Linear Equations

General Theory of nth Order Linear Equations

Homogeneous Equations with Constant Coef?cients

The Method of Undetermined Coef?cients

The Method of Variation of Parameters

Series Solutions of Second Order Linear Equations

Review of Power Series

Series Solutions Near an Ordinary Point, Part I

Series Solutions Near an Ordinary Point, Part II

Euler Equations

Regular Singular Points

Series Solutions Near a Regular Singular Point, Part I

Series Solutions Near a Regular Singular Point, Part II

Bessel's Equation

The Laplace Transform

Definition of the Laplace Transform

Solution of Initial Value Problems

Step Functions

Differential Equations with Discontinuous Forcing Functions

Impulse Functions

The Convolution Integral

Systems of First Order Linear Equations

Introduction

Review of Matrices

Systems of Linear Algebraic Equations

Linear Independence, Eigenvalues, Eigenvectors

Basic Theory of Systems of First Order Linear Equations

Homogeneous Linear Systems with Constant Coefficients

Complex Eigenvalues

Fundamental Matrices

Repeated Eigenvalues

Nonhomogeneous Linear Systems

Numerical Methods

The Euler or Tangent Line Method

Improvements on the Euler Method

The Runge-Kutta Method

Multistep Methods

More on Errors

Stability

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