A First Course in Fourier Analysis
Cambridge University Press
Edition: 2, 1/17/2008
EAN 9780521709798, ISBN10: 0521709792
Paperback, 862 pages, 24.4 x 17.8 x 4.3 cm
Language: English
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.
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.