Transform Methods for Solving Partial Differential Equations

ISBN: 9781584884514 出版年：2004 页码：727 Duffy, Dean G CRC Press

THE FUNDAMENTALS Fourier Transforms Laplace Transforms Linear Ordinary Differential Equations Complex Variables Multivalued Functions, Branch Points, Branch Cuts, and Riemann Surfaces Some Examples of Integration which Involve Multivalued Functions Bessel Functions What are Transform Methods? METHODS INVOLVING SINGLE-VALUED LAPLACE TRANSFORMS Inversion of Laplace Transforms by Contour Integration The Heat Equation The Wave Equation Laplace's and Poisson's Equations Papers Using Laplace Transforms to Solve Partial Differential Equations METHODS INVOLVING SINGLE-VALUED FOURIER AND HANKEL TRANSFORMS Inversion of Fourier Transforms by Contour Integration The Wave Equation The Heat Equation Laplace's Equation The Solution of Partial Differential Equations by Hankel Transforms Numerical Inversion of Hankel Transforms Papers Using Fourier Transforms to Solve Partial Differential Equations Papers Using Hankel Transforms to Solve Partial Differential Equations METHODS INVOLVING MULTIVALUED LAPLACE TRANSFORMS Inversion of Laplace Transforms by Contour Integration Numerical Inversion of Laplace Transforms The Wave Equation The Heat Equation Papers Using Laplace Transforms to Solve Partial Differential Equations METHODS INVOLVING MULTIVALUED FOURIER TRANSFORMS Inversion of Fourier Transforms by Contour Integration Numerical Inversion of Fourier Transforms The Solution of Partial Differential Equations by Fourier Transforms Papers Using Fourier Transforms to Solve Partial Differential Equations THE JOINT TRANSFORM METHOD The Wave Equation The Heat and Other Partial Differential Equations Inversion of the Joint Transform by Cagniard's Method The Modification of Cagniard's Method by De Hoop Papers Using the Joint Transform Technique Papers Using the Cagniard Technique Papers Using the Cagniard-De Hoop Technique THE WIENER-HOPF TECHNIQUE The Wiener-Hopf Technique When the Factorization Contains No Branch Points The Wiener-Hopf Technique when the Factorization Contains Branch Points Papers Using the Wiener-Hopf Technique WORKED SOLUTIONS TO SOME OF THE PROBLEMS INDEX