Fourier Series and Integral Transforms

Fourier Series and Integral Transforms

by Allan Pinkus, Samy Zafrany
     
 

ISBN-10: 0521592097

ISBN-13: 9780521592093

Pub. Date: 09/01/1997

Publisher: Cambridge University Press

The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course…  See more details below

Overview

The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.

Product Details

ISBN-13:
9780521592093
Publisher:
Cambridge University Press
Publication date:
09/01/1997
Pages:
200
Product dimensions:
5.98(w) x 8.98(h) x 0.63(d)

Table of Contents

Preface
0Notation and Terminology1
1Basic Concepts in Set Theory1
2Calculus Notation2
3Useful Trigonometric Formulae4
1Background: Inner Product Spaces5
1Linear and Inner Product Spaces5
2The Norm10
3Orthogonal and Orthonormal Systems15
4Orthogonal Projections and Approximation in the Mean19
5Infinite Orthonormal Systems24
2Fourier Series32
1Definitions32
2Evenness, Oddness, and Additional Examples40
3Complex Fourier Series42
4Pointwise Convergence and Dirichlet's Theorem46
5Uniform Convergence56
6Parseval's Identity63
7The Gibbs Phenomenon68
8Sine and Cosine Series72
9Differentiation and Integration of Fourier Series76
10Fourier Series on Other Intervals81
11Applications to Partial Differential Equations85
3The Fourier Transform93
1Definitions and Basic Properties93
2Examples98
3Properties and Formulae102
4The Inverse Fourier Transform and Plancherel's Identity108
5Convolution116
6Applications of the Residue Theorem119
7Applications to Partial Differential Equations125
8Applications to Signal Processing130
4The Laplace Transform140
1Definition and Examples140
2More Formulae and Examples143
3Applications to Ordinary Differential Equations149
4The Heaviside and Dirac-Delta Functions155
5Convolution162
6More Examples and Applications168
7More Inverse Transform Formula173
8Applications of the Inverse Transform175
App. AThe Residue Theorem and Related Results182
App. BLeibniz's Rule and Fubini's Theorem186
Index188

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >