Elementary Differential Equations, 7th Edition, Active Learning Edition Set

by William E. Boyce (Rensselaer Polytechnic Institute)

• ISBN13: 9780471308409
• ISBN10: 0471308404
• Edition: 7th
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Wiley

Summary

Textbook: Written with an applied mathematics approach, this marketing leading text is designed for a sophomore - junior level course in Ordinary Differential Equations. Focusing on the theory and practical applications of Differential Equations as they apply to engineering and the sciences, this edition continues in the successful tradition of previous editions. It offers a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Concepts are reorganized and represented to be even clearer and more comprehensible. An abundance of new problems have been added to the problem sets, with special attention paid to incorporating computer technology. (Textbook ISBN: 0471308404) Student Solutions Manual: This manual contains solutions to selected problems in the text, providing invaluable guidance as you work through the problems and master the materials presented in the text. (Student Solutions Manual ISBN: 047139114X)

Author Biography

William E. Boyce is the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer Richard C. DiPrima is on the faculty of Rensselaer Polytechnic Institute

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-KuttaMethod

Multistep Methods

More on Errors; Stability

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