An Introduction to Laplace Transforms and Fourier Series

by Dyke, P. P. G.

• ISBN13: 9781852330156
• ISBN10: 1852330155
• Format: Paperback
• Copyright: 1999-12-01
• Publisher: Springer Verlag

Summary

This book is a self-contained introduction to Laplace Transforms and Fourier Series; emphasising the applications of Laplace transforms throughout, the book also provides coverage of the underlying pure mathematical structures. Alongside the Laplace transform, the notion of Fourier series is developed from first principles. Exercises are provided to consolidate understanding of the concepts and techniques, and only a knowledge of elementary calculus and trigonometry is assumed. For second and third year students looking for a rigorous and practical introduction to the subject, this book will be an invaluable source.

Table of Contents

The Laplace Transform	p. 1
Further Properties of the Laplace Transform	p. 13
Convolution and the Solution of Ordinary Differential Equations	p. 37
Fourier Series	p. 77
Partial Differential Equations	p. 109
Fourier Transforms	p. 127
Complex Variables and Laplace Transforms	p. 155
A: Solutions to Exercises	p. 183
Table of Laplace Transforms	p. 225
Linear Spaces	p. 229
Bibliography	p. 243
Index	p. 245
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