Integral Transforms and Their Applications

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CRC Press, Jul 3, 1995 - Mathematics - 480 pages
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Integral Transforms and Their Applications, provides a systematic , comprehensive review of the properties of integral transforms and their applications to the solution of boundary and initial value problems. Over 750 worked examples, exercises, and applications illustrate how transform methods can be used to solve problems in applied mathematics, mathematical physics, and engineering. The specific applications discussed include problems in differential, integral, and difference equations; electric circuits and networks; vibrations and wave propagation; heat conduction; fractional derivatives and fractional integrals; dynamical systems; signal processing; quantum mechanics; atmosphere and ocean dynamics; physical chemistry; mathematical biology; and probability and statistics.
Integral Transforms and Their Applications includes broad coverage the standard material on integral transforms and their applications, along with modern applications and examples of transform methods. It is both an ideal textbook for students and a sound reference for professionals interested in advanced study and research in the field.
 

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Contents

Fourier Transforms
5
Laplace Transforms
83
Applications of Laplace Transforms
123
Hankel Transforms
193
Mellin Transforms
211
Hilbert and Stieltjes Transforms
237
Finite Fourier Cosine and Sine Transforms
265
Finite Laplace Transforms
283
Legendre Transforms
325
Jacobi and Gegenbauer Transforms
337
Laguerre Transforms
345
Hermite Transforms
355
Appendix A Some Special Functions and Their Properties
367
Appendix B Tables of Integral Transforms
387
Answers and Hints to Selected Exercises
423
Bibliography
441

Z Transforms
295
Finite Hankel Transforms
317

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