Integral Transforms and their Applications

Front Matter....Pages N2-xv
Definition and Elementary Properties....Pages 1-14
The Inversion Theorem....Pages 15-25
Ordinary Differential Equations....Pages 26-46
Partial Differential Equations....Pages 47-58
Integral Equations....Pages 59-75
The Inversion Integral....Pages 76-88
Definitions and Elementary Properties....Pages 89-109
Application to Partial Differential Equations....Pages 110-129
Generalized Functions....Pages 130-154
Green’a Functions....Pages 155-177
Fourier Transforms in Two or More Variables....Pages 178-194
Mellin Transforms....Pages 195-213
Mellin Transforms in Summation....Pages 214-224
Integrals Involving a Parameter....Pages 225-236
Hankel Transforms....Pages 237-253
Dual Integral Equations....Pages 254-266
Integral Transforms Generated by Green’s Functions....Pages 267-287
The Wiener-Hopf Technique....Pages 288-312
Methods Based on Cauchy Integrals....Pages 313-341
Laplace’s Method for Ordinary Differential Equations....Pages 342-373
Numerical Inversion of Laplace Transforms....Pages 374-395
Back Matter....Pages 396-416