A First Course in Fourier Analysis

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

This unique book introduces 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. 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.

Inhaltsverzeichnis

1. Fourier's representation for functions on R, Tp, Z, and PN; 2. Convolution of functions on R, Tp, Z and PN; 3. The calculus for finding Fourier transforms of functions of R; 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN; 5. Operator identities associated with Fourier analysis; 6. The fast Fourier transform; 7. Generalized functions on R; 8. Sampling; 9. Partial differential equations; 10. Wavelets; 11. Musical tones; 12. Probability; Appendix 0. The impact of Fourier analysis; Appendix 1. Functions and their Fourier transforms; Appendix 2. The Fourier transform calculus; Appendix 3. Operators and their Fourier transforms; Appendix 4. The Whittaker-Robinson flow chart for harmonic analysis; Appendix 5. FORTRAN code for a Radix 2 FFT; Appendix 6. The standard normal probability distribution; Appendix 7. Frequencies of the piano keyboard; Index.

Erscheinungsjahr:	2011
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	862
ISBN-13:	9780521709798
ISBN-10:	0521709792
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Kammler, David W.
Auflage:	Revised
Hersteller:	Cambridge University Press
Maße:	244 x 170 x 46 mm
Von/Mit:	David W. Kammler
Erscheinungsdatum:	10.08.2011
Gewicht:	1,456 kg

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