Integral Transforms and Their Applications, Second Edition

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CRC Press, Oct 11, 2006 - Mathematics - 728 pages
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Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises.

The most significant changes in the second edition include:

  • New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform
  • Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle
  • A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions
  • A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject

    A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.
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    Contents

    Integral Transforms
    1
    Fourier Transforms and Their Applications
    9
    Laplace Transforms and Their Basic Properties
    133
    Applications of Laplace Transforms
    181
    Fractional Calculus and Its Applications
    269
    Applications of Integral Transforms to Fractional Dfferential and Integral Equations
    283
    Hankel Transforms and Their Applications
    315
    Mellin Transforms and Their Applications
    339
    Legendre Transforms
    485
    Jacobi and Gegenbauer Transforms
    501
    Laguerre Transforms
    511
    Hermite Transforms
    525
    The Radon Transform and Its Applications
    539
    Wavelets and Wavelet Transforms
    563
    Some Special Functions and Their Properties
    587
    Tables of Integral Transforms
    611

    Hilbert and Stieltjes Transforms
    371
    Finite Fourier Sine and Cosine Transforms
    407
    Finite Laplace Transforms
    429
    Z Transforms
    445
    Finite Hankel Transforms
    473
    Answers and Hints to Selected Exercises
    645
    Bibliography
    673
    Index
    689
    Copyright

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