Book:Peter D. Robinson/Fourier and Laplace Transforms

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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