Integral Transforms and Their ApplicationsIntegral Transforms and Their Applications, provides a systematic , comprehensive review of the properties of integral transforms and their applications to the solution of boundary and initial value problems. Over 750 worked examples, exercises, and applications illustrate how transform methods can be used to solve problems in applied mathematics, mathematical physics, and engineering. The specific applications discussed include problems in differential, integral, and difference equations; electric circuits and networks; vibrations and wave propagation; heat conduction; fractional derivatives and fractional integrals; dynamical systems; signal processing; quantum mechanics; atmosphere and ocean dynamics; physical chemistry; mathematical biology; and probability and statistics. Integral Transforms and Their Applications includes broad coverage the standard material on integral transforms and their applications, along with modern applications and examples of transform methods. It is both an ideal textbook for students and a sound reference for professionals interested in advanced study and research in the field. |
Contents
Fourier Transforms | 5 |
7 | 32 |
9 | 113 |
Applications of Laplace Transforms | 123 |
64 | 154 |
Laplace Transforms | 166 |
Hankel Transforms | 193 |
6 | 206 |
Finite Hankel Transforms | 317 |
Legendre Transforms | 325 |
Jacobi and Gegenbauer Transforms | 337 |
Laguerre Transforms | 345 |
Hermite Transforms | 355 |
Appendix A Some Special Functions and Their Properties | 367 |
Appendix B Tables of Integral Transforms | 387 |
Answers and Hints to Selected Exercises | 423 |
Hilbert and Stieltjes Transforms | 237 |
Finite Fourier Cosine and Sine Transforms | 265 |
Finite Laplace Transforms | 283 |
Z Transforms | 295 |
| 441 | |
| 449 | |
Common terms and phrases
amplitude Application asymptotic basic operational properties beam boundary conditions boundary value problem c-joo constant Convolution Theorem cosh Debnath definition difference equation erfc Example exp x² finite Fourier sine finite Laplace transform fluid formal solution formula Fourier cosine transform Fourier sine transform fractional derivative fractional integral frequency function f(x ƒ ƒ given gives the formal gives the solution 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 Laplace transform gives Legendre linear mathematical Mellin transform obtain the solution ordinary differential equation oscillations polynomials Proof result satisfies Show sinh Stieltjes transform transform with respect u₁ velocity wave equation Z transform zero ηπ ди дх