9781584884514

Transform Methods for Solving Partial Differential Equations, Second Edition

by ;
  • ISBN13:

    9781584884514

  • ISBN10:

    1584884517

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2004-07-15
  • Publisher: Chapman & Hall/

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Summary

Transform Methods for Solving Partial Differential Equations illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. This second edition is expanded to provide a broader perspective on the applicability and use of transform methods. It classifies the problems presented in every chapter by type of region, coordinate system and partial differential equation. Many of the problems included in the book are illustrated to show the reader what they will look like physically. Unlike many mathematics texts, this book provides a step-by-step analysis of problems taken from the actual scientific and engineering literature.

Table of Contents

1 The Fundamentals 1(60)
1.1 Fourier Transforms
1(6)
1.2 Laplace Transforms
7(6)
1.3 Linear Ordinary Differential Equations
13(3)
1.4 Complex Variables
16(8)
1.5 Multivalued Functions, Branch Points, Branch Cuts and Riemann Surfaces
24(2)
1.6 Some Examples of Integration That Involve Multivalued Functions
26(23)
1.7 Bessel Functions
49(5)
1.8 What Are Transform Methods?
54(7)
2 Methods Involving Single-Valued Laplace Transforms 61(160)
2.1 Inversion of Laplace Transforms by Contour Integration
61(17)
2.2 The Heat Equation
78(63)
2.3 The Wave Equation
141(41)
2.4 Laplace's and Poisson's Equations
182(39)
Papers Using Laplace Transforms to Solve Partial Differential Equations
191(30)
3 Methods Involving Single-Valued Fourier and Hankel Transforms 221(86)
3.1 Inversion of Fourier Transforms by Contour Integration
221(15)
3.2 The Wave Equation
236(9)
3.3 The Heat Equation
245(5)
3.4 Laplace's Equation
250(20)
3.5 The Solution of Partial Differential Equations by Hankel Transforms
270(23)
3.6 Numerical Inversion of Hankel Transforms
293(14)
Papers Using Fourier Transforms to Solve Partial Differential Equations
302(3)
Papers Using Hankel Transforms to Solve Partial Differential Equations
305(2)
4 Methods Involving Multivalued Laplace Transforms 307(118)
4.1 Inversion of Laplace Transforms by Contour Integration
307(65)
4.2 Numerical Inversion of Laplace Transforms
372(14)
4.3 The Wave Equation
386(8)
4.4 The Heat Equation
394(31)
Papers Using Laplace Transforms to Solve Partial Differential Equations
416(9)
5 Methods Involving Multivalued Fourier Transforms 425(46)
5.1 Inversion of Fourier Transforms by Contour Integration
425(19)
5.2 Numerical Inversion of Fourier Transforms
444(10)
5.3 Solution of Partial Differential Equations
454(17)
Papers Using Fourier Transforms to Solve Partial Differential Equations
468(3)
6 The Joint Transform Method 471(94)
6.1 The Wave Equation
471(25)
6.2 The Heat and Other Partial Differential Equations
496(13)
6.3 Inversion of the Joint Transform by Cagniard's Method
509(14)
6.4 The Modification of Cagniard's Method by De Hoop
523(42)
Papers Using the Joint Transform Technique
544(9)
Papers Using the Cagniard Technique
553(4)
Papers Using the Cagniard-De Hoop Technique
557(8)
7 The Wiener-Hopf Technique 565(62)
7.1 The Wiener-Hopf Technique When the Factorization Contains No Branch Points
571(20)
7.2 The Wiener-Hopf Technique When the Factorization Contains Branch Points
591(36)
Papers Using the Wiener-Hopf Technique
605(22)
Worked Solutions to Some of the Problems 627(78)
Index 705

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