Integral Transforms and Their ApplicationsKeeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering. |
Contents
1 | |
9 | |
Laplace Transforms and Their Basic Properties | 133 |
Applications of Laplace Transforms | 181 |
Fractional Calculus and Its Applications | 269 |
Applications of Integral Transforms to Fractional Dfferential and Integral Equations | 283 |
Hankel Transforms and Their Applications | 315 |
Mellin Transforms and Their Applications | 339 |
Legendre Transforms | 485 |
Jacobi and Gegenbauer Transforms | 501 |
Laguerre Transforms | 511 |
Hermite Transforms | 525 |
The Radon Transform and Its Applications | 539 |
Wavelets and Wavelet Transforms | 563 |
Some Special Functions and Their Properties | 587 |
Tables of Integral Transforms | 611 |
Hilbert and Stieltjes Transforms | 371 |
Finite Fourier Sine and Cosine Transforms | 407 |
Finite Laplace Transforms | 429 |
Z Transforms | 445 |
Finite Hankel Transforms | 473 |
Answers and Hints to Selected Exercises | 645 |
673 | |
689 | |
Other editions - View all
Integral Transforms and Their Applications, Second Edition Lokenath Debnath,Dambaru Bhatta Limited preview - 2006 |
Common terms and phrases
amplitude Application Basic Operational Properties boundary conditions boundary value problem c+ ioo Cauchy coefficients constant Convolution Theorem cosh Debnath definition diffusion equation evaluation Exercises finite Fourier sine finite Hankel transform finite Laplace transform fluid formal solution Fourier cosine transform Fourier sine transform fractional calculus fractional derivative fractional integral frequency function f(x given gives the solution Haar wavelet Hankel transform Heaviside Hence Hilbert transform Hint initial conditions initial data initial value problem integral equation integral transforms inverse Fourier transform inverse Laplace transform inverse transform joint Laplace Laguerre transform Legendre transform linear mathematical Mellin transform operational calculus partial differential equations plane polynomial prove Radon transform result satisfies Show Similarly sinh Stieltjes transform theory transfer function Transform and Examples transform solution transform with respect velocity wave equation wavelet transform zero
Popular passages
Page 3 - Theorem, which is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth's crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.