A First Course in Fourier Analysis
A First Course in Fourier Analysis
$104.00
USDThis 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.
- A modern introduction to Fourier analysis and its applications: shows how Fourier analysis can be used to study sampling theory, PDEs, probability, diffraction and real-world applications
- Accessible to students and researchers in mathematics, physics, chemistry, geology and engineering
- Over 540 exercises illustrate and extend mathematical ideas from the text, stimulating the development of problem-solving skills
Product details
January 2008Paperback
9780521709798
862 pages
244 × 178 × 43 mm
1.47kg
211 b/w illus. 3 tables 545 exercises
Available
Table of 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.
