Overview
- Illustrates how the theory of distributions can be applied to solve problems in the physical and engineering sciences
- Includes a robust selection of example problems that can arise in real-life industrial and scientific labs
- Will be a valuable resource for researchers and graduate students who would like more exposure to probabilistic methods
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Keywords
- Theory of Distributions
- Anomalous fractional random dynamics
- Generalized stochastic processes and fields
- Random Distributions
- Burgers Turbulence
- Passive Tracer Transport
About this book
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The goal of the books is to give the reader, specialist and non-specialist usable and modern mathematical tools in their research and analysis.
Volume 1 provides detailed coverage of asymptotic methods, including the stationary phase and steepest descent methods, for Fourier and other integral transforms from an application perspective. Other topics covered include fractional calculus, the uncertainty principle, wavelets, and multiresolution analysis.
Volume 2 contains an analysis of the three basic types of linear PDEs - elliptic, parabolic, and hyperbolic - as well as chapters on first-order nonlinearPDEs and conservation laws. Nonlinear waves, Burger's equations, KdV equations, and the equations of gas dynamics and porous media are also covered.
Volume 3 extends the scope to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media.
The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book isideal for a general scientific and engineering audience, yet it is mathematically precise.
Volume 1 provides detailed coverage of asymptotic methods, including the stationary phase and steepest descent methods, for Fourier and other integral transforms from an application perspective. Other topics covered include fractional calculus, the uncertainty principle, wavelets, and multiresolution analysis.
Volume 2 contains an analysis of the three basic types of linear PDEs - elliptic, parabolic, and hyperbolic - as well as chapters on first-order nonlinearPDEs and conservation laws. Nonlinear waves, Burger's equations, KdV equations, and the equations of gas dynamics and porous media are also covered.
Volume 3 extends the scope to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media.
The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book isideal for a general scientific and engineering audience, yet it is mathematically precise.
Authors and Affiliations
About the authors
Alexander I. Saichev was Professor of Mathematics at the Radio Physics Faculty of the Nizhny Novgorod University and a Professor in the Department of Management, Technology, and Economics at the Swiss Federal Institute of Technology.
Wojbor A. Woyczynski is Professor of Mathematics and Director of the Center for Stochastic and Chaotic Processes in Science and Technology at Case Western University.
Wojbor A. Woyczynski is Professor of Mathematics and Director of the Center for Stochastic and Chaotic Processes in Science and Technology at Case Western University.
Bibliographic Information
Book Title: Distributions in the Physical and Engineering Sciences
Book Subtitle: Volumes 1-3
Authors: Alexander I. Saichev, Wojbor A Woyczynski
Publisher: Birkhäuser Cham
Copyright Information: Springer Nature Switzerland AG 2019
Edition Number: 1