國立虎尾科技大學 |

Distributions in the Physical and Engineering Sciences, Volume 3 = Random and Anomalous Fractional Dynamics in Continuous Media /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Distributions in the Physical and Engineering Sciences, Volume 3/ by Alexander I. Saichev, Wojbor A. woyczyński.
Reminder of title:	Random and Anomalous Fractional Dynamics in Continuous Media /
Author:	Saichev, Alexander I.
other author:	woyczyński, Wojbor A.
Description:	XX, 403 p. 61 illus., 6 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1007/978-3-319-92586-8
ISBN:	9783319925868

Distributions in the Physical and Engineering Sciences, Volume 3 = Random and Anomalous Fractional Dynamics in Continuous Media /
Saichev, Alexander I.

Distributions in the Physical and Engineering Sciences, Volume 3Random and Anomalous Fractional Dynamics in Continuous Media /[electronic resource] :by Alexander I. Saichev, Wojbor A. woyczyński. - 1st ed. 2018. - XX, 403 p. 61 illus., 6 illus. in color.online resource. - Applied and Numerical Harmonic Analysis,2296-5009. - Applied and Numerical Harmonic Analysis,.

Introduction to Volume 3 -- Notation -- Basic Distributional Tools for Probability Theory -- Random Distributions: Generalized Stochastic Processes -- Dynamical and Statistical Characteristics of Random Fields and Waves -- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows -- Probability Distributions of Passive Tracers in Randomly Moving Media -- Levy Processes and Their Generalized Derivatives -- Linear Anomalous Fractional Dynamics in Continuous Media -- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media -- Appendix A: Basic Facts About Distributions -- Bibliography -- Index.

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.

ISBN: 9783319925868

Standard No.: 10.1007/978-3-319-92586-8doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Distributions in the Physical and Engineering Sciences, Volume 3 = Random and Anomalous Fractional Dynamics in Continuous Media /
LDR:04225nam a22004335i 4500 001 992020
003 DE-He213
005 20200630064634.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319925868 $9 978-3-319-92586-8
024 7 $a 10.1007/978-3-319-92586-8 $2 doi
035 $a 978-3-319-92586-8
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Saichev, Alexander I. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1078627
245 1 0 $a Distributions in the Physical and Engineering Sciences, Volume 3 $h [electronic resource] : $b Random and Anomalous Fractional Dynamics in Continuous Media / $c by Alexander I. Saichev, Wojbor A. woyczyński.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2018.
300 $a XX, 403 p. 61 illus., 6 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Applied and Numerical Harmonic Analysis, $x 2296-5009
505 0 $a Introduction to Volume 3 -- Notation -- Basic Distributional Tools for Probability Theory -- Random Distributions: Generalized Stochastic Processes -- Dynamical and Statistical Characteristics of Random Fields and Waves -- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows -- Probability Distributions of Passive Tracers in Randomly Moving Media -- Levy Processes and Their Generalized Derivatives -- Linear Anomalous Fractional Dynamics in Continuous Media -- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media -- Appendix A: Basic Facts About Distributions -- Bibliography -- Index.
520 $a 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.
650 0 $a Probabilities. $3 527847
650 0 $a Engineering mathematics. $3 562757
650 0 $a Functional analysis. $3 527706
650 0 $a Statistics . $3 1253516
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Engineering Mathematics. $3 1203947
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. $3 782247
700 1 $a woyczyński, Wojbor A. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1283699
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319925844
776 0 8 $i Printed edition: $z 9783319925851
776 0 8 $i Printed edition: $z 9783030064679
830 0 $a Applied and Numerical Harmonic Analysis, $x 2296-5009 $3 1254485
856 4 0 $u https://doi.org/10.1007/978-3-319-92586-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)