A First Course in Fourier Analysis Book

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.