# Book:Peter D. Robinson/Fourier and Laplace Transforms

## Peter D. Robinson: *Fourier and Laplace Transforms*

Published $1968$, **Routledge and Kegan Paul**.

### Subject Matter

### 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