Book:Peter D. Robinson/Fourier and Laplace Transforms

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