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

ISBN: 9780495108368 / 0495108367

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1,600 ### 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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