An Introduction to Integral Transforms

Content: 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 Parsevalâ€
™
s Relations For Fourier Transforms --
1.13 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 Function --
2.4 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 Property. 3.9 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 Tricomiâ€
™
smethod. --
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 --
5.4 Relation Between Hilbert Transform And Fourier Transform --
5.5 Finite Hilbert Transform --
5.6 One-sided Hilbert Transform --
5.7 Asymptotic Expansions Of One-sided Hilbert Transform --
5.8 The Stieltjes Transform --
5.9 Some Deductions --
5.10 The Inverse Stieltjes Transform --
5.11 Relation Between Hilbert Transform And Stieltjes Transform. --
Chapter 6. Hankel Transforms --
6.1 Introduction --
6.2 The Hankel Transform --
6.3 Elementary Properties --
6.4 Inversion Formula For Hankel Transform --
6.5 The Parseval Relation For Hankel Transforms --
6.6 Illustrative Examples --
Chapter 7. Finite Hankel Transforms --
7.1 Introduction. 7.2 Expansion Of Some Functions In Series Involving Cylinder Functions : Fourier-bessel Series --
7.3 The Finite Hankel Transform --
7.4 Illustrative Examples --
7.5 Finite Hankel Transform Of Order N In 0 X 1 Of The Derivatrive Of A Function --
7.6 Finite Hankel Transform Over 0 X1 Of Order N Of D2f Dx2x Df Dx , When P Is The Root Of Jn(p) = 0 --
7.7 Finite Hankel Transform Of F (x --
Xf (x) --
N2 X2 F (x), Where P Is The Root Of Jn(p) = 0 In 0 X 1 --
7.8 Other Forms Of Finite Hankel Transforms --
7.9 Illustrations --
7.10 Application Of Finite Hankel Transforms --
Chapter 8. The Mellin Transform --
8.1 Introduction --
8.2 Definition Of Mellin Transform --
8.3 Mellin Transform Of Derivative Of A Function --
8.4 Mellin Transform Of Integral Of A Function --
8.5 Mellin Inversion Theorem --
8.6 Convolution Theorem Of Mellin Transform --
8.7 Illustrative Solved Examples --
8.8 Solution Of Integral Equations --
8.9 Application To Summation Of Series --
8.10 The Generalised Mellin Transform --
8.11 Convolution Of Generalised Mellin Transform --
8.12 Finite Mellin Transform --
Chapter 9. Finite Laplace Transforms --
9.1 Introduction --
9.2 Definition Of Finite Laplace Transform --
9.3 Finite Laplace Transform Of Elementary Functions --
9.4 Operational Properties --
9.5 The Initial Value And The Final Value Theorem --
9.6 Applications --
Chapter 10. Legendre Transforms --
10.1 Introduction --
10.2 Definition Of Legendre Transform --
10.3 Elementary Properties Of Legendre Transforms --
10.4 Operational Properties Of Legendre Transforms --
10.5 Application To Boundary Value Problems --
Chapter 11. The Kontorovich-lebedev Transform --
11.1 Introduction --
11.2 Definition Of Kontorovich --
Lebedev Transform --
11.3 Parseval Relation For Kontorovich-lebedev Transforms --
11.4 Illustrative Examples. 11.5 Boundary Value Problem In A Wedge Of Finite Thickness --
Chapter 12. The Mehler-fock Transform --
12.1 Introduction --
12.2 Fockâ€
™
s Theorem(with Weaker Restriction --
12.3 Mehler-fock Transform Of Zero Order And Its Properties --
12.4 Parseval Type Relation --
12.5 Mehler-fock Transform Of Order M --
12.6 Application To Boundary Value Problems --
12.6.1 First Example --
12.6.2 Second Example --
12.6.3 Third Example --
12.6.4 Fourth Example --
12.7 Application Of Mehler-fock Transform For Solving Dual Integral Equation --
Chapter 13. Jacobi, Gegenbauer, Laguerre And Hermite Transforms --
13.1 Introduction --
13.2 Definition Of Jacobi Transform --
13.3 The Gegenbauer Transform --
13.4 Convolution Theorem --
13.5 Application Of The Transforms --
13.6 The Laguerre Transform --
13.7 Operational Properties --
13.8 Hermite Transform --
13.9 Operational Properties --
13.10hermite Transform Of Derivative Of A Function --
Chapter 14. The Z-transform --
14.1 Introduction --
14.2 Z --
Transform: Definition --
14.3 Some Operational Properties Of Z-transform --
14.4 Application Of Z-transforms --
Appendix --
Bibliography --
Index.