Contents of the first edition
Fourier Series and Integral Transforms
Allan Pinkus
and
Samy Zafrany
Now Available from
Cambridge University Press.
for further information and ordering details:
Cambridge University Press (U.S.A.)
.
TABLE OF CONTENTS
Chapter 0: Notation and Terminology

Basic Concepts in Set Theory

Calculus Notation

Useful Trigonometric Formulae
Chapter 1: Background: Inner Product Spaces

Introduction

Linear and Inner Product Spaces

The Norm

Orthogonal and Orthonormal Systems

Orthogonal Projections and Approximation in the Mean

Infinite Orthonormal Systems

Review Exercises
Chapter 2 Fourier Series

Introduction

Definitions

Evenness, Oddness, and Additional Examples

Complex Fourier Series

Pointwise Convergence and Dirichlet's Theorem

Uniform Convergence

Parseval's Identity

The Gibbs Phenomenon

Sine and Cosine Series

Differentiation and Integration of Fourier Series

Fourier Series on Other Intervals

Applications to Partial Differential Equations

Review Exercises
Chapter 3 The Fourier Transform

Introduction

Definitions and Basic Properties

Examples

Properties and Formulae

The Inverse Fourier Transform and Plancherel's Identity

Convolution

Applications of the Residue Theorem

Applications to Partial Differential Equations

Applications to Signal Processing

Review Exercises
Chapter 4: The Laplace Transform

Introduction

Definition and Examples

More Formulae and Examples

Applications to Ordinary Differential Equations

The Heaviside and DiracDelta Functions

Convolution

More Examples and Applications

The Inverse Transform Formula

Applications of the Inverse Transform

Review Exercises
Appendix A: The Residue Theorem and Related Results
Appendix B: Leibniz's Rule and Fubini's Theorem