An introduction to integral transforms /
"'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...
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| Format: | eBook |
| Language: | English |
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Boca Raton, FL :
CRC Press,
[2018]
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Half Title; Title; Copyrights; Dedication; Preface; Acknowledgement; Contents; Chapter 1. Fourier Transform; 1.1 Introduction; 1.2 Classes Of Functions; 1.3 Fourier Series And Fourier Integral Formula; 1.4 Fourier Transforms; 1.4.1 Fourier Sine And Cosine Transforms; 1.5 Linearity Property Of Fourier Transforms; 1.6 Change Of Scale Property; 1.7 Themodulation Theorem; 1.8 Evaluation Of Integrals By Means Of Inversion Theorems; 1.9 Fourier Transform Of Some Particular Functions; 1.10 Convolution Or Faltung Of Two Integrable Functions; 1.11 Convolution Or Falting Or Faltung Theoremfor Ft.
- 1.12 Parsevalâs Relations For Fourier Transforms1.13 Fourier Transform Of The Derivative Of A Function; 1.14 Fourier Transform Of Some More Useful Functions; 1.15 Fourier Transforms Of Rational Functions; 1.16 Other Important Examples Concerning Derivative Of Ft; 1.17 The Solution Of Integral Equations Of Convolution Type; 1.18 Fourier Transformof Functions Of Several Variables; 1.19 Application Of Fourier Transform To Boundary Value Problems; Chapter 2. Finite Fourier Transform; 2.1 Introduction; 2.2 Finite Fourier Cosine And Sine Transforms.
- 2.3 Relation Between Finite Fourier Transform Of The Derivatives Of A Function2.4 Faltung Or Convolution Theorems For Finite Fourier Transform.; 2.5 Multiple Finite Fourier Transform; 2.6 Double Transforms Of Partial Derivatives Of Functions; 2.7 Application Of Finite Fourier Transforms To Boundary Value Problems; Chapter 3. The Laplace Transform; 3.1 Introduction; 3.2 Definitions; 3.3 Sufficient Conditions For Existence Of Laplace Transform; 3.4 Linearity Property Of Laplace Transform; 3.5 Laplace Transforms Of Some Elementary Functions; 3.6 First Shift Theorem; 3.7 Second Shift Theorem.
- 3.8 The Change Of Scale Property3.9 Examples; 3.10 Laplace Transform Of Derivatives Of A Function; 3.11 Laplace Transform Of Integral Of A Function; 3.12 Laplace Transform Of Tnf(t; 3.13 Laplace Transform Of F(t)/t; 3.14 Laplace Transform Of A Periodic Function; 3.15 The Initial-value Theorem And The Final-value Theorem Of Laplace Transform; 3.16 Examples; 3.17 Laplace Transform Of Some Special Functions; 3.18 The Convolution Of Two Functions; 3.19 Applications; Chapter 4. The Inverse Laplace Transform And Application; 4.1 Introduction.
- 4.2 Calculation Of Laplace Inversion Of Some Elementary Functions. 4.3 Method Of Expansion Into Partial Fractions Of The Ratio Of Two Polynomials; 4.4 The General Evaluation Technique Of Inverse Laplace Transform.; 4.5 Inversion Formula From A Different Stand Point : The Tricomiâs method.; 4.6 The Double Laplace Transform; 4.7 The Iterative Laplace Transform; 4.8 The Bilateral Laplace Transform; 4.9 Application Of Laplace Transforms; Chapter 5. Hilbert And Stieltjes Transforms; 5.1 Introduction; 5.2 Definition Of Hilbert Transform; 5.3 Some Important Properties Of Hilbert Transforms.