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Applied and Numerical Harmonic Analysis

Distributions in the Physical and Engineering Sciences, Volume 3

Random and Anomalous Fractional Dynamics in Continuous Media

Authors: Saichev, Alexander I., Woyczynski, Wojbor A

  • 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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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-92586-8
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-319-92584-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences.  Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media.  With this volume, the scope is extended 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 needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts.
Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas.  The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed.  An appendix also provides background material concerning the Dirac-delta and other distributions.

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.

Table of contents (8 chapters)

  • Basic Distributional Tools for Probability Theory

    Saichev, Alexander I. (et al.)

    Pages 3-62

  • Random Distributions: Generalized Stochastic Processes

    Saichev, Alexander I. (et al.)

    Pages 63-98

  • Dynamical and Statistical Characteristics of Random Fields and Waves

    Saichev, Alexander I. (et al.)

    Pages 99-129

  • Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows

    Saichev, Alexander I. (et al.)

    Pages 131-183

  • Probability Distributions of Passive Tracers in Randomly Moving Media

    Saichev, Alexander I. (et al.)

    Pages 185-240

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-92586-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-319-92584-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Distributions in the Physical and Engineering Sciences, Volume 3
Book Subtitle
Random and Anomalous Fractional Dynamics in Continuous Media
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-92586-8
DOI
10.1007/978-3-319-92586-8
Hardcover ISBN
978-3-319-92584-4
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XX, 403
Number of Illustrations and Tables
55 b/w illustrations, 6 illustrations in colour
Topics