Solution Techniques for Elementary Partial Differential Equations, Second Edition

by Constanda; Christian

• ISBN13: 9781439811399
• ISBN10: 1439811393
• Edition: 2nd
• Format: Nonspecific Binding
• Copyright: 2010-06-14
• Publisher: Chapman & Hall/

Summary

This popular text presents some of the most important and widely used methods for solving PDEs. Along with a new chapter on complex variable methods, this edition includes new sections on Cauchy'Euler equations, Bessel functions, Legendre polynomials, spherical harmonics, applications of Fourier transformations, and general hyperbolic equations. It lists additional mathematical models based on PDEs and shows how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace. The author also added many new worked examples and exercises. Ancillary materials are available for qualifying instructors.

Table of Contents

Foreword	p. xi
Preface to the Second Edition	p. xiii
Preface to the First Edition	p. xv
Ordinary Differential Equations: Brief Review	p. 1
First-Order Equations	p. 1
Homogeneous Linear Equations with Constant Coefficients	p. 3
Nonhomogeneous Linear Equations with Constant Coefficients	p. 5
Cauchy-Euler Equations	p. 6
Functions and Operators	p. 7
Exercises	p. 9
Fourier Series	p. 11
The Full Fourier Series	p. 11
Fourier Sine Series	p. 17
Fourier Cosine Series	p. 21
Convergence and Differentiation	p. 23
Exercises	p. 24
Sturm-Liouville Problems	p. 27
Regular Sturm-Liouville Problems	p. 27
Other Problems	p. 39
Bessel Functions	p. 41
Legendre Polynomials	p. 47
Spherical Harmonics	p. 50
Exercises	p. 54
Some Fundamental Equations of Mathematical Physics	p. 59
The Heat Equation	p. 59
The Laplace Equation	p. 67
The Wave Equation	p. 73
Other Equations	p. 78
Exercises	p. 81
The Method of Separation of Variables	p. 83
The Heat Equation	p. 83
The Wave Equation	p. 95
The Laplace Equation	p. 101
Other Equations	p. 109
Equations with More than Two Variables	p. 113
Exercises	p. 124
Linear Nonhomogeneous Problems	p. 131
Equilibrium Solutions	p. 131
Nonhomogeneous Problems	p. 136
Exercises	p. 140
The Method of Eigenfunction Expansion	p. 143
The Heat Equation	p. 143
The Wave Equation	p. 149
The Laplace Equation	p. 152
Other Equations	p. 155
Exercises	p. 159
The Fourier Transformations	p. 165
The Full Fourier Transformation	p. 165
The Fourier Sine and Cosine Transformations	p. 172
Other Applications	p. 179
Exercises	p. 181
The Laplace Transformation	p. 187
Definition and Properties	p. 187
Applications	p. 192
Exercises	p. 202
The Method of Green's Functions	p. 205
The Heat Equation	p. 205
The Laplace Equation	p. 213
The Wave Equation	p. 217
Exercises	p. 223
General Second-Order Linear Partial Differential Equations with Two Independent Variables	p. 227
The Canonical Form	p. 227
Hyperbolic Equations	p. 231
Parabolic Equations	p. 235
Elliptic Equations	p. 238
Exercises	p. 239
The Method of Characteristics	p. 241
First-Order Linear Equations	p. 241
First-Order Quasilinear Equations	p. 248
The One-Dimensional Wave Equation	p. 249
Other Hyperbolic Equations	p. 256
Exercises	p. 260
Perturbation and Asymptotic Methods	p. 263
Asymptotic Series	p. 263
Regular Perturbation Problems	p. 266
Singular Perturbation Problems	p. 274
Exercises	p. 280
Complex Variable Methods	p. 285
Elliptic Equations	p. 285
Systems of Equations	p. 291
Exercises	p. 294
Answers to Odd-Numbered Exercises	p. 297
Appendix	p. 313
Bibliography	p. 319
Index	p. 321
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