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.
Number of Pages: 862 Format(s): Paperback - ISBN: 9780521709798 Publication Date:17/01/2008 Listed in:Calculus & mathematical analysis Publisher:CAMBRIDGE UNIVERSITY PRESS