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A First Course in Fourier Analysis

2nd Edition


  • Date Published: January 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521709798

£ 66.99

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About the Authors
  • 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.

    • 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
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    Product details

    • Edition: 2nd Edition
    • Date Published: January 2008
    • format: Paperback
    • isbn: 9780521709798
    • length: 862 pages
    • dimensions: 244 x 178 x 43 mm
    • weight: 1.47kg
    • contains: 211 b/w illus. 3 tables 545 exercises
    • availability: 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

  • Author

    David W. Kammler, Southern Illinois University, Carbondale

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