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patra b introduction integral transform 2018

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Textbook in PDF format 'An Introduction to Integral Transforms' is meant for students pursuing graduate and post graduate studies in Science and Engineering. It contains discussions on almost all transforms for normal users of the subject. The content of the book is explained from a rudimentary stand point to an advanced level for convenience of its readers. Pre‐requisite for understanding the subject matter of the book is some knowledge on the complex variable techniques. Cover Half Title Title Copyrights Dedication Preface Acknowledgement Fourier Transform Introduction Classes Of Functions Fourier Series And Fourier Integral Formula Fourier Transforms Fourier Sine And Cosine Transforms Linearity Property Of Fourier Transforms Change Of Scale Property Themodulation Theorem Evaluation Of Integrals By Means Of Inversion Theorems Fourier Transform Of Some Particular Functions Convolution Or Faltung Of Two Integrable Functions Convolution Or Falting Or Faltung Theorem for Ft Parseval's Relations For Fourier Transforms Fourier Transform Of The Derivative Of A Function Fourier Transform Of Some More Useful Functions Fourier Transforms Of Rational Functions Other Important Examples Concerning Derivative Of Ft The Solution Of Integral Equations Of Convolution Type Fourier Transformof Functions Of Several Variables Application Of Fourier Transform To Boundary Value Problems Finite Fourier Transform Introduction Finite Fourier Cosine And Sine Transforms Relation Between Finite Fourier Transform Of The Derivatives Of A Function Faltung Or Convolution Theorems For Finite Fourier Transform Multiple Finite Fourier Transform Double Transforms Of Partial Derivatives Of Functions Application Of Finite Fourier Transforms To Boundary Value Problems The Laplace Transform Introduction Definitions Sufficient Conditions For Existence Of Laplace Transform Linearity Property Of Laplace Transform Laplace Transforms Of Some Elementary Functions First Shift Theorem Second Shift Theorem The Change Of Scale Property Examples Laplace Transform Of Derivatives Of A Function Laplace Transform Of Integral Of A Function Laplace Transform Of Tnf(t Laplace Transform Of F(t)/t Laplace Transform Of A Periodic Function The Initial-value Theorem And The Final-value Theorem Of Laplace Transform Examples Laplace Transform Of Some Special Functions The Convolution Of Two Functions Applications The Inverse Laplace Transform And Application Introduction Calculation Of Laplace Inversion Of Some Elementary Functions Method Of Expansion Into Partial Fractions Of The Ratio Of Two Polynomials The General Evaluation Technique Of Inverse Laplace Transform Inversion Formula From A Different Stand Point : The Tricomi's method The Double Laplace Transform The Iterative Laplace Transform The Bilateral Laplace Transform Application Of Laplace Transforms Hilbert And Stieltjes Transforms Introduction Definition Of Hilbert Transform Some Important Properties Of Hilbert Transforms Relation Between Hilbert Transform And Fourier Transform Finite Hilbert Transform One-sided Hilbert Transform Asymptotic Expansions Of One-sided Hilbert Transform The Stieltjes Transform Some Deductions The Inverse Stieltjes Transform Relation Between Hilbert Transform And Stieltjes Transform Hankel Transforms Introduction The Hankel Transform Elementary Properties Inversion Formula For Hankel Transform The Parseval Relation For Hankel Transforms Illustrative Examples Finite Hankel Transforms Introduction Expansion Of Some Functions In Series Involving Cylinder Functions : Fourier-bessel Series The Finite Hankel Transform Illustrative Examples Finite Hankel Transform Of Order N In X Of The Derivatrive Of A Function Finite Hankel Transform Over X Of Order N Of Df Dxx Df Dx , When P Is The Root Of Jn(p) = Finite Hankel Transform Of F (x Xf (x) N X F (x), Where P Is The Root Of Jn(p) = In X Other Forms Of Finite Hankel Transforms Illustrations Application Of Finite Hankel Transforms The Mellin Transform Introduction Definition Of Mellin Transform Mellin Transform Of Derivative Of A Function Mellin Transform Of Integral Of A Function Mellin Inversion Theorem Convolution Theorem Of Mellin Transform Illustrative Solved Examples Solution Of Integral Equations Application To Summation Of Series The Generalised Mellin Transform Convolution Of Generalised Mellin Transform Finite Mellin Transform Finite Laplace Transforms Introduction Definition Of Finite Laplace Transform Finite Laplace Transform Of Elementary Functions Operational Properties The Initial Value And The Final Value Theorem Applications Legendre Transforms Introduction Definition Of Legendre Transform Elementary Properties Of Legendre Transforms Operational Properties Of Legendre Transforms Application To Boundary Value Problems The Kontorovich-lebedev Transform Introduction Definition Of Kontorovich Lebedev Transform Parseval Relation For Kontorovich-lebedev Transforms Illustrative Examples Boundary Value Problem In A Wedge Of Finite Thickness The Mehler-fock Transform Introduction Focka's Theorem(with Weaker Restriction Mehler-fock Transform Of Zero Order And Its Properties Parseval Type Relation Mehler-fock Transform Of Order M Application To Boundary Value Problems First Example Second Example Third Example Fourth Example Application Of Mehler-fock Transform For Solving Dual Integral Equation Jacobi, Gegenbauer, Laguerre And Hermite Transforms Introduction Definition Of Jacobi Transform The Gegenbauer Transform Convolution Theorem Application Of The Transforms The Laguerre Transform Operational Properties Hermite Transform Operational Properties hermite Transform Of Derivative Of A Function The Z-transform Introduction Z-Transform: Definition Some Operational Properties Of Z-transform Application Of Z-transforms Appendix Bibliography Index

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patra b introduction integral transform 2018