Book:Peter D. Robinson/Fourier and Laplace Transforms

Peter D. Robinson: Fourier and Laplace Transforms

Published $\text {1968}$, Routledge and Kegan Paul

Subject Matter

• Fourier Analysis
• Laplace Transforms

Contents

Preface

Chapter One: Introduction

$1.1$ The idea of an integral transform

$1.2$ The usefulness of an integral transform

$1.3$ Fourier Series and Finite Fourier Transforms

$1.4$ The flow of heat in a uniform bar

$1.5$ The limiting case: an infinite bar

$1.6$ The Fourier Transforms

$1.7$ The Laplace Transforms

$1.8$ Other transforms

$1.9$ Evaluating transforms

Exercises

Chapter Two: Further Theory

$2.1$ Transforms of Convolutions

$2.2$ Parseval's Formulae for Fourier Transforms

$2.3$ Scaling theorems

$2.4$ Translation theorems

$2.5$ Tranforms of derivatives

$2.6$ Derivatives and integrals of transforms

$2.7$ Worked examples

Exercises

Chapter Three: Linear Differential Equations

$3.1$ Ordinary differential equations with constant coefficients

$3.2$ Ordinary differential equations with variable coefficients

$3.3$ The diffusion equation in one dimension

$3.4$ The wave equation in one dimension

$3.5$ Further partial differential equations

Exercises

Chapter Four: Linear Integral Equations

$4.1$ Introduction

$4.2$ Integral equations of the first kind with difference kernels

$4.3$ Integral equations of the second kind with difference kernels

$4.4$ Other similar differential equations

Exercises

Appendix A: A sketch proof of Fourier's Integral Formula

References

Tables of transforms

Table 1. Sine transforms

Table 2. Cosine Transforms

Table 3. Fourier Transforms

Table 4. Laplace Transforms

Answers to exercises

Index

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