Amazon no longer offers textbook rentals. We do!

Schaum's Outline of Differential Equations, 3rd edition

by: Bronson, Richard

Schaum's Outline of Differential Equations, 3rd edition

by: Bronson, Richard

ISBN 13:
9780071456876
ISBN 10:
0071456872
Edition: 2nd
Format: Paperback
Copyright: 06/15/2006
Publisher: McGraw-Hill

Rent

Sorry, this item is currently unavailable on Knetbooks.com

Click the link below to purchase this eBook from our trusted partner, eCampus.com.

View eBook

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Extend or Purchase Your Rental at Any Time

Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.

Summary

Solve differential equations faster and easier! Thoroughly updated, this third edition of "Schaum's Outline of Differential Equations" offers you new, faster techniques for solving differential equations generated by the emergence of high-speed computers. Differential equations, a linchpin of modern math, are essential in engineering, the natural sciences, economics, and business. Includes: 563 fully solved problems 800-plus supplementary problems New chapter on modeling

Basic Concepts

(8)

Differential Equations

(1)

Notation

(1)

Solutions

(1)

Initial-Value and Boundary-Value Problems

(7)

An Introduction to Modeling and Qualitative Methods

(5)

Mathematical Models

(1)

The ``Modeling Cycle''

(1)

Qualitative Methods

(4)

Classifications of First-Order Differential Equations

(7)

Standard Form and Differential Form

(1)

Linear Equations

(1)

Bernoulli Equations

(1)

Homogeneous Equations

(1)

Separable Equations

(1)

Exact Equations

(6)

Separable First-Order Differential Equations

(10)

General Solution

(1)

Solutions to the Initial-Value Problem

(1)

Reduction of Homogeneous Equations

(9)

Exact First-Order Differential Equations

(11)

Defining Properties

(1)

Method of Solution

(1)

Integrating Factors

(10)

Linear First-Order Differential Equations

(8)

Method of Solution

(1)

Reduction of Bernoulli Equations

(8)

Applications of First-Order Differential Equations

(23)

Growth and Decay Problems

(1)

Temperature Problems

(1)

Falling Body Problems

(1)

Dilution Problems

(1)

Electrical Circuits

(1)

Orthogonal Trajectories

(20)

Linear Differential Equations: Theory of Solutions

(10)

Linear Differential Equations

(1)

Linearly Independent Solutions

(1)

The Wronskian

(1)

Nonhomogeneous Equations

(9)

Second-Order Linear Homogeneous Differential Equations with Constant Coefficients

(6)

Introductory Remark

(1)

The Characteristic Equation

(1)

The General Solution

(5)

nth-Order Linear Homogeneous Differential Equations with Constant Coefficients

(5)

The Characteristic Equation

(1)

The General Solution

(4)

The Method of Undetermined Coefficients

(9)

Simple Form of the Method

(1)

Generalizations

(1)

Modifications

(1)

Limitations of the Method

(8)

Variation of Parameters

103

(7)

The Method

103

(1)

Scope of the Method

104

(6)

Initial-Value Problems for Linear Differential Equations

110

(4)

Applications of Second-Order Linear Differential Equations

114

(17)

Spring Problems

114

(1)

Electrical Circuit Problems

115

(1)

Buoyancy Problems

116

(1)

Classifying Solutions

117

(14)

Matrices

131

(9)

Matrices and Vectors

131

(1)

Matrix Addition

131

(1)

Scalar and Matrix Multiplication

132

(1)

Powers of a Square Matrix

132

(1)

Differentiation and Integration of Matrices

132

(1)

The Characteristic Equation

133

(7)

eAt

140

(8)

Definition

140

(1)

Computation of eAt

140

(8)

Reduction of Linear Differential Equations to a System of First-Order Equations

148

(9)

An Example

148

(1)

Reduction of an nth Order Equation

149

(1)

Reduction of a System

150

(7)

Graphical and Numerical Methods for Solving First-Order Differential Equations

157

(19)

Qualitative Methods

157

(1)

Direction Fields

157

(1)

Euler's Method

158

(1)

Stability

158

(18)

Further Numerical Methods for Solving First-Order Differential Equations

176

(19)

General Remarks

176

(1)

Modified Euler's Method

177

(1)

Runge--Kutta Method

177

(1)

Adams--Bashford--Moulton Method

177

(1)

Milne's Method

177

(1)

Starting Values

178

(1)

Order of a Numerical Method

178

(17)

Numerical Methods for Solving Second-Order Differential Equations Via Systems

195

(16)

Second-Order Differential Equations

195

(1)

Euler's Method

196

(1)

Runge--Kutta Method

196

(1)

Adams--Bashford--Moulton Method

196

(15)

The Laplace Transform

211

(13)

Definition

211

(1)

Properties of Laplace Transforms

211

(1)

Functions of Other Independent Variables

212

(12)

Inverse Laplace Transforms

224

(9)

Definition

224

(1)

Manipulating Denominators

224

(1)

Manipulating Numerators

225

(8)

Convolutions and the Unit Step Function

233

(9)

Convolutions

233

(1)

Unit Step Function

233

(1)

Translations

234

(8)

Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms

242

(7)

Laplace Transforms of Derivatives

242

(1)

Solutions of Differential Equations

243

(6)

Solutions of Linear Systems by Laplace Transforms

249

(5)

The Method

249

(5)

Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods

254

(8)

Solution of the Initial-Value Problem

254

(1)

Solution with No Initial Conditions

255

(7)

Power Series Solutions of Linear Differential Equations with Variable Coefficients

262

(13)

Second-Order Equations

262

(1)

Analytic Functions and Ordinary Points

262

(1)

Solutions Around the Origin of Homogeneous Equations

263

(1)

Solutions Around the Origin of Nonhomogeneous Equations

263

(1)

Initial-Value Problems

264

(1)

Solutions Around Other Points

264

(11)

Series Solutions Near a Regular Singular Point

275

(15)

Regular Singular Points

275

(1)

Method of Frobenius

275

(1)

General Solution

276

(14)

Some Classical Different Equations

290

(5)

Classical Differential Equations

290

(1)

Polynomial Solutions and Associated Concepts

290

(5)

Gamma and Bessel Functions

295

(9)

Gamma Function

295

(1)

Bessel Functions

295

(1)

Algebraic Operations on Infinite Series

296

(8)

An Introduction to Partial Differential Equations

304

(5)

Introductory Concepts

304

(1)

Solutions and Solution Techniques

305

(4)

Second-Order Boundary-Value Problems

309

(9)

Standard Form

309

(1)

Solutions

310

(1)

Eigenvalue Problems

310

(1)

Sturm--Liouville Problems

310

(1)

Properties of Sturm--Liouville Problems

310

(8)

Eigenfunction Expansions

318

(7)

Piecewise Smooth Functions

318

(1)

Fourier Sine Series

319

(1)

Fourier Cosine Series

319

(6)

An Introduction to Difference Equations

325

(5)

Introduction

325

(1)

Classifications

325

(1)

Solutions

326

(4)

APPENDIX A Laplace Transforms

330

(6)

APPENDIX B Some Comments about Technology

336

(2)

Introductory Remarks

336

(1)

T1-89

337

(1)

Mathematica

337

(1)

Answers to Supplementary Problems

338

(44)

Index

382

Amazon no longer offers textbook rentals. We do!

Schaum's Outline of Differential Equations, 3rd edition

Schaum's Outline of Differential Equations, 3rd edition

9780071456876

0071456872

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Schaum's Outline of Differential Equations, 3rd edition

Schaum's Outline of Differential Equations, 3rd edition

9780071456876

0071456872

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Related Products