Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications.
New to the Third Edition
- New material on the historical development of classical and modern integral transforms
- New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle
- Revised material on Laplace transforms and double Laplace transforms and their applications
- New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more
- New figures that facilitate a clear understanding of physical explanations
- Updated exercises with solutions, tables of integral transforms, and bibliography
Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.
Table of Contents
Integral Transforms. Fourier Transforms and Their Applications. Laplace Transforms and Their Basic Properties. Applications of Laplace Transforms. Fractional Calculus and Its Applications. Applications of Integral Transforms to Fractional Differential Equations. Hankel Transforms and Their Applications. Mellin Transforms and Their Applications. Hilbert and Stieltjes Transforms. Finite Fourier Sine and Cosine Transforms. Finite Laplace Transforms. Z Transforms. Finite Hankel Transforms. Legendre Transforms. Jacobi and Gegenbauer Transforms. Laguerre Transforms. Hermite Transforms. The Radon Transform and Its Application. Wavelets and Wavelet Transforms. Appendices.