## Integral Transforms and Their ApplicationsIntegral 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 |

441 | |

### Common terms and phrases

Application asymptotic axisymmetric basic operational properties beam Bessel function biharmonic equation boundary conditions boundary value problem Cauchy change of variable characteristic function constant Convolution Theorem cosh Debnath definition difference equation evaluation Find the solution finite Fourier sine finite Hankel transform finite Laplace transform fluid formal solution Fourier cosine transform Fourier sine transform Fourier transform gives fractional derivative fractional integral frequency function f(x gives the formal gives the solution Hankel transform Heaviside Heaviside's Hence Hilbert transform Hint initial conditions initial data initial value problem integral equation integral transforms inverse Fourier transform inverse Laplace transform inverse transform Laguerre transform Legendre transform linear mathematical Mellin transform obtain the solution operational calculus physical plane Proof prove random variable result satisfies Show Similarly Stieltjes transform transform defined transform method transform to solve transform with respect velocity wave equation Z transform zero