Paperback. This 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. Introducing applied mathematics through Fourier analysis, this book develops a unified theory of discrete and continuous 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title: A First Course in Fourier Analysis (Paperback)
Publisher: Cambridge University Press, Cambridge
Publication Date: 2008
Language: English
ISBN 10: 0521709792
ISBN 13: 9780521709798
Binding: Paperback
Edition: 2nd Edition
Condition: new

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Synopsis

This book introduces applied mathematics through Fourier analysis, with applications to studying sampling theory, PDEs, probability, diffraction, musical tones, and wavelets.

Book Description

Introducing applied mathematics through Fourier analysis, this book develops a unified theory of discrete and continuous 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.

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