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A First Course in Fourier Analysis, 2nd Edition

A First Course in Fourier Analysis, 2nd Edition

by David W. Kammler

2007 (864 pages)

ISBN:9780521883405

Developing a unified theory of discrete and continuous Fourier analysis, fast Fourier transform, and a powerful elementary theory of generalized functions, this unique text shows how they can be used to study sampling theory, PDEs, probability, and more.

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Table of Contents

A First Course in Fourier Analysis, 2nd Edition
Mathematics—Source and Substance
Preface
The Mathematical Core
Chapter 1	-	Fourier’s Representation for Functions on R, Tp, Z, and PN
Chapter 2	-	Convolution of Functions on R, Tp, Z, and PN
Chapter 3	-	The Calculus for Finding Fourier Transforms of Functions on R
Chapter 4	-	The Calculus for Finding Fourier Transforms of Functions on Tp, Z, and PN
Chapter 5	-	Operator Identities Associated with Fourier Analysis
Chapter 6	-	The Fast Fourier Transform
Chapter 7	-	Generalized Functions on R
Selected Applications
Chapter 8	-	Sampling
Chapter 9	-	Partial Differential Equations
Chapter 10	-	Wavelets
Chapter 11	-	Musical Tones
Chapter 12	-	Probability
Appendices
Appendix 1	-	The Impact of Fourier Analysis
Appendix 2	-	Functions and Their Fourier Transforms
Appendix 3	-	The Fourier Transform Calculus
Appendix 4	-	Operators and Their Fourier Transforms
Appendix 5	-	The Whittaker—Robinson Flow Chart for Harmonic Analysis
Appendix 6	-	FORTRAN Code for a Radix 2 FFT
Appendix 7	-	The Standard Normal Probability Distribution
Appendix 8	-	Frequencies of the Piano Keyboard