Articoli correlati a A First Course in Fourier Analysis
Sinossi
This book introduces applied mathematics through Fourier analysis, with applications to studying sampling theory, PDEs, probability, diffraction, musical tones, and wavelets.
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Descrizione del libro
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.
Contenuti
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.
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