Integral Transforms in Applied Mathematics

John W. Miles

doi:10.1017/CBO9780511897351

An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided.

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Integral Transforms in Applied Mathematics

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Contents

Frontmatter
pp i-iv

PREFACE
pp v-vi

Contents
pp vii-x

Dedication
pp xi-xii

1 - INTEGRAL-TRANSFORM PAIRS
pp 1-12

2 - THE LAPLACE TRANSFORM
pp 13-42

3 - FOURIER TRANSFORMS
pp 43-56

4 - HANKEL TRANSFORMS
pp 57-66

5 - FINITE FOURIER TRANSFORMS
pp 67-78

APPENDIX 1 - PARTIAL-FRACTION EXPANSIONS
pp 79-82

APPENDIX 2 - TABLES
pp 83-86

APPENDIX 3 - LIST OF NOTATIONS
pp 87-88

GLOSSARY
pp 89-89

BIBLIOGRAPHY
pp 90-94

INDEX
pp 95-97

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