INTEGRAL TRANSFORMS AND THEIR APPLICATIONS is about four important integral transforms, viz., Fourier transform, Laplace transform, Mellin transform and Hankel transform together with their application. These four integral transforms have been defined and their inversion formulas have been derived. They have been used in finding the solution of many physical problems. These problems include evolution of some definite integrals, integral equations involving Fourier kernel, solution of some partial differential equations with given initial and boundary condition which are of importance in mathematical physics.

• Laplace transform like initial value theorem and final value theorem have been stated and proved • Asymptotic expansion of Laplace inversion integral has been developed • Two sided Laplace transform of a function has been discussed • The Mellin and Hankel transform of a function of real variable for all its positive real values including zero have been defined • Demonstrated with examples.

Preface / FOURIER TRANSFORM: Fourier Transform / Fourier Sine and Cosine Transform / Finite Fourier Transform / Multiple Fourier Transform / Application to Partial Differential Equations / LAPLACE TRANSFORM: Basic Properties of Laplace Transform / The Inverse Laplace Transform / Two-Sided Laplace Transform / Solution of Linear Differential Equations / Linear Integral Equation of Convolution Type / MELLIN TRANSFORM: Definition and Properties of Mellin Transform / The Inverse Mellin Transform / Applications / HANKEL TRANSFORM: Hankel Transform / Finite Hankel Transform / Index.

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