Fourier Series and Integral Transforms

Front Cover
Cambridge University Press, Jul 10, 1997 - Mathematics - 189 pages
1 Review
This volume provides 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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Selected pages

Contents

Notation and Terminology
1
2 Calculus Notation
2
3 Useful Trigonometric Formulae
4
Background Inner Product Spaces
5
2 The Norm
10
3 Orthogonal and Orthonormal Systems
15
4 Orthogonal Projections and Approximation in the Mean
19
5 Infinite Orthonormal Systems
24
The Fourier Transform
93
2 Examples
98
3 Properties and Formulae
102
4 The Inverse Fourier Transform and Plancherels Identity
108
6 Applications of the Residue Theorem
119
7 Applications to Partial Differential Equations
125
8 Applications to Signal Processing
130
The Laplace Transform
140

Fourier Series
32
2 Evenness Oddness and Additional Examples
40
3 Complex Fourier Series
42
4 Pointwise Convergence and Dirichlets Theorem
46
5 Uniform Convergence
56
6 Parsevals Identity
63
7 The Gibbs Phenomenon
68
8 Sine and Cosine Series
72
9 Differentiation and Integration of Fourier Series
76
10 Fourier Series on Other Intervals
81
11 Applications to Partial Differential Equations
85
2 More Formulae and Examples
143
3 Applications to Ordinary Differential Equations
149
4 The Heaviside and DiracDelta Functions
155
5 Convolution
162
6 More Examples and Applications
168
7 The Inverse Transform Formula
173
8 Applications of the Inverse Transform
175
The Residue Theorem and Related Results
182
Leibnizs Rule and Fubinis Theorem
186
Index
188
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information