Differential Equations with Boundary-Value Problems, 7th Edition

Differential Equations with Boundary-Value Problems ... Differential Equations with Boundary-Value ...

ISBN: 9780495108368 / 0495108367

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Table of Contents

Chapter 1

Introduction To Differential Equations

1.1 Definitions and Terminology Exercises p.10
1.2 Initial-Value Problems Exercises p.17
1.3 Differential Equations as Mathematical Models Exercises p.27
Chapter 1 in Review p.32

Chapter 2

First-Order Differential Equations

2.1 Solution Curves Without a Solution Exercises p.41
2.2 Separable Equations Exercises p.50
2.3 Linear Equations Exercises p.60
2.4 Exact Equations Exercises p.68
2.5 Solutions By Substitutions Exercises p.74
2.6 A Numerical Method Exercises p.79
Chapter 2 in Review p.80

Chapter 3

Modeling With First-Order Differential Equations

3.1 Linear Models Exercises p.89
3.2 Nonlinear Models Exercises p.99
3.3 Modeling with Systems of First-Order DEs Exercises p.110
Chapter 3 in Review p.113

Chapter 4

Higher-Order Differential Equations

4.1 Preliminary Theory - Linear Equations Exercises p.128
4.2 Reduction of Order Exercises p.132
4.3 Homogeneous Linear Equations with Constant Coefficients Exercises p.138
4.4 Undetermined Coefficients - Superposition Approach Exercises p.148
4.5 Undetermined Coefficients - Annihilator Approach Exercises p.156
4.6 Variation of Parameters Exercises p.161
4.7 Cauchy-Euler Equation Exercises p.168
4.8 Solving Systems of Linear Des by Elemination Exercises p.172
4.9 Nonlinear Differential Equations Exercises p.177
Chapter 4 in Review p.178

Chapter 5

Modeling With Higher-Order Differential Equations

5.1 Linear Models: Initial-Value Problems Exercises p.194
5.2 Linear Models: Boundary-Value Problems Exercises p.204
5.3 Nonlinear Models Exercises p.213
Chapter 5 in Review p.216

Chapter 6

Series Solutions Of Linear Equations

6.1 Solutions About Ordinary Points Exercises p.230
6.2 Solutions about Singular Points Exercises p.239
6.3 Special Functions Exercises p.250
Chapter 6 in Review p.253

Chapter 7

The Laplace Transform

7.1 Definition of the Laplace Transform Exercises p.261
7.2 Inverse Transforms and Transforms of Derivatives Exercises p.269
7.3 Operation Properties I Exercises p.278
7.4 Operational Properties II Exercises p.289
7.5 The Dirac Delta Function Exercises p.295
7.6 Systems of Linear Differential Equations Exercises p.299
Chapter 7 in Review p.300

Chapter 8

Systems Of Linear First-Order Differential Equations

8.1 Preliminary Theory - Linear Systems Exercises p.310
8.2 Homogeneous Linear Systems Exercises p.324
8.3 Nonhomogeneous Linear Systems Exercises p.332
8.4 Matrix Exponential Exercises p.336
Chapter 8 in Review p.337

Chapter 9

Numerical Solutions Of Ordinary Differential Equations

9.1 Euler Methods and Error Analysis Exercises p.344
9.2 Runge-Kutta Methods Exercises p.348
9.3 Multistep Methods Exercises p.353
9.4 Higher-Order Equations and Systems Exercises p.357
9.5 Second-Order Boundary-Value Problems Exercises p.361
Chapter 9 in Review p.362

Chapter 10

Plane Autonomous Systems

10.1 Autonomous Systems Exercises p.369
10.2 Stability of Linear Systems Exercises p.377
10.3 Linearization and Local Stability Exercises p.386
10.4 Autonomous Systems as Mathematical Models Exercises p.393
Chapter 10 in Review p.395

Chapter 11

Fourier Series

11.1 Orthogonal Functions Exercises p.402
11.2 Fourier Series Exercises p.407
11.3 Fourier Cosine and Sine Series Exercises p.414
11.4 Sturm-Liouville Problem Exercises p.422
11.5 Bessel and Legendre Series Exercises p.429
Chapter 11 in Review p.430

Chapter 12

Boundary-Value Problems In Rectangular Coordinates

12.1 Separable Partial Differential Equations Exercises p.436
12.2 Classical PDEs and Boundary-Value Problems Exercises p.442
12.3 Heat Equation Exercises p.445
12.4 Wave Equation Exercises p.448
12.5 Laplace's Equation Exercises p.454
12.6 Nonhomogeneous Boundary-Value Problems Exercises p.459
12.7 Orthogonal Series Expansions Exercises p.465
12.8 Higher-Dimensional Problems Exercises p.469
Chapter 12 in Review p.469

Chapter 13

Boundary-Value Problems In Other Coordinate Systems

13.1 Polar Coordinates Exercises p.475
13.2 Polar and Cylindrical Coordinates Exercises p.481
13.3 Spherical Coordinates Exercises p.485
Chapter 13 in Review p.486

Chapter 14

Integral Transforms

14.1 Error Function Exercises p.490
14.2 Laplace Transform Exercises p.495
14.3 Fourier Integral Exercises p.503
14.4 Fourier Transforms Exercises p.508
Chapter 14 in Review p.510

Chapter 15

Numerical Solutions Of Partial Differential Equations

15.1 Laplace's Equation Exercises p.517
15.2 Heat Equation Exercises p.521
15.3 Wave Equation Exercises p.525
Chapter 15 in Review p.526
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