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Integral Transforms and Their Applications

  • Book
  • © 1978

Overview

Authors:
  1. B. Davies

    1. The Australian National University, Canberra, Australia

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Part of the book series: Applied Mathematical Sciences (AMS, volume 25)

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Table of contents (21 chapters)

  1. Front Matter

    Pages N2-xii
    Download chapter PDF

  2. The Laplace Transform

    1. Definition and Elementary Properties

      • B. Davies
      Pages 1-14

    2. The Inversion Theorem

      • B. Davies
      Pages 15-25

    3. Ordinary Differential Equations

      • B. Davies
      Pages 26-46

    4. Partial Differential Equations

      • B. Davies
      Pages 47-58

    5. Integral Equations

      • B. Davies
      Pages 59-75

    6. The Inversion Integral

      • B. Davies
      Pages 76-88

  3. The Fourier Transform

    1. Definitions and Elementary Properties

      • B. Davies
      Pages 89-109

    2. Application to Partial Differential Equations

      • B. Davies
      Pages 110-129

    3. Generalized Functions

      • B. Davies
      Pages 130-154

    4. Green’s Functions

      • B. Davies
      Pages 155-177

    5. Fourier Transforms in Two or More Variables

      • B. Davies
      Pages 178-194

  4. Other Important Transforms

    1. Mellin Transforms

      • B. Davies
      Pages 195-213

    2. Mellin Transforms in Summation

      • B. Davies
      Pages 214-224

    3. Integrals Involving a Parameter

      • B. Davies
      Pages 225-236

    4. Hankel Transforms

      • B. Davies
      Pages 237-253

    5. Dual Integral Equations

      • B. Davies
      Pages 254-266

    6. Integral Transforms Generated by Green’s Functions

      • B. Davies
      Pages 267-287

  5. Special Techniques

    1. The Wiener-Hopf Technique

      • B. Davies
      Pages 288-312

    2. Methods Based on Cauchy Integrals

      • B. Davies
      Pages 313-341
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About this book

This book is intended to serve as introductory and reference material for the application of integral transforms to a range of common mathematical problems. It has its im­ mediate origin in lecture notes prepared for senior level courses at the Australian National University, although I owe a great deal to my colleague Barry Ninham, a matter to which I refer below. In preparing the notes for publication as a book, I have added a considerable amount of material ad- tional to the lecture notes, with the intention of making the book more useful, particularly to the graduate student - volved in the solution of mathematical problems in the physi­ cal, chemical, engineering and related sciences. Any book is necessarily a statement of the author's viewpoint, and involves a number of compromises. My prime consideration has been to produce a work whose scope is selective rather than encyclopedic; consequently there are many facets of the subject which have been omitted--in not a few cases after a preliminary draft was written--because I v believe that their inclusion would make the book too long.

Authors and Affiliations

  • The Australian National University, Canberra, Australia

    B. Davies

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