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First Course in Fourier Analysis

ISBN-10: 0521709792

ISBN-13: 9780521709798

Edition: 2nd 2007 (Revised)

Authors: David W. Kammler

List price: $89.99
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Description:

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
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Book details

List price: $89.99
Edition: 2nd
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 1/17/2008
Binding: Paperback
Pages: 862
Size: 7.00" wide x 9.75" long x 1.75" tall
Weight: 3.432
Language: English

Serge-Christophe Kolm is Professor of Economics at the Ecole des Hautes Etudes en Sciences Sociales, Paris.

Fourier's representation for functions on R, Tp, Z, and PN
Convolution of functions on R, Tp, Z and PN
The calculus for finding Fourier transforms of functions of R
The calculus for finding Fourier transforms of functions of Tp, Z, and PN
Operator identities associated with Fourier analysis
The fast Fourier transform
Generalized functions on R
Sampling
Partial differential equations
Wavelets
Musical tones
Probability
The impact of Fourier analysis
Functions and their Fourier transforms
The Fourier transform calculus
Operators and their Fourier transforms
The Whittaker-Robinson flow chart for harmonic analysis
FORTRAN code for a Radix 2 FFT
The standard normal probability distribution
Frequencies of the piano keyboard
Index