David W. Kammler

A First Course in Fourier Analysis

• Broschiertes Buch

Produktbeschreibung

This unique book introduces applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourieranalysis, 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.

Produktdetails

• Verlag: Cambridge University Press
• 2., überarb. Aufl.
• Seitenzahl: 862
• Erscheinungstermin: 10. August 2011
• Englisch
• Abmessung: 244mm x 170mm x 46mm
• Gewicht: 1460g
• ISBN-13: 9780521709798
• ISBN-10: 0521709792
• Artikelnr.: 22864349

Inhaltsangabe

From the contents:
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.