04287nam a22005895i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001600188072002300204082001200227100003700239245012600276264004600402300003600448336002600484337002600510338003600536347002400572490005100596505090300647520134201550650001702892650002702909650002802936650003602964650002603000650001903026650001303045650002503058650002903083650001703112650001403129650003603143650004903179650005903228650003703287650004303324700003103367710003403398773002003432776003603452830005103488856004803539912001403587999001903601952007703620978-0-387-73829-1DE-He21320180115171416.0cr nn 008mamaa100301s2008 xxu| s |||| 0|eng d a97803877382919978-0-387-73829-17 a10.1007/978-0-387-73829-12doi 4aQA299.6-433 7aPBK2bicssc 7aMAT0340002bisacsh04a5152231 aPavliotis, Grigorios A.eauthor.10aMultiscale Methodsh[electronic resource] :bAveraging and Homogenization /cby Grigorios A. Pavliotis, Andrew M. Stuart. 1aNew York, NY :bSpringer New York,c2008. aXVIII, 310 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aTexts Applied in Mathematics,x0939-2475 ;v530 aBackground -- Analysis -- Probability Theory and Stochastic Processes -- Ordinary Differential Equations -- Markov Chains -- Stochastic Differential Equations -- Partial Differential Equations -- Perturbation Expansions -- Invariant Manifolds for ODEs -- Averaging for Markov Chains -- Averaging for ODEs and SDEs -- Homogenization for ODEs and SDEs -- Homogenization for Elliptic PDEs -- Homogenization for Parabolic PDEs -- Averaging for Linear Transport and Parabolic PDEs -- Theory -- Invariant Manifolds for ODEs: The Convergence Theorem -- Averaging for Markov Chains: The Convergence Theorem -- Averaging for SDEs: The Convergence Theorem -- Homogenization for SDEs: The Convergence Theorem -- Homogenization for Elliptic PDEs: The Convergence Theorem -- Homogenization for Elliptic PDEs: The Convergence Theorem -- Averaging for Linear Transport and Parabolic PDEs: The Convergence Theorem. aThis introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. The book begins by setting the theoretical foundations of the subject area, and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions. The presentation of the material is particularly suited to the range of mathematicians, scientists and engineers who want to exploit multiscale methods in applications. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable readers to build their own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter. All of the twenty-one chapters are supplemented with exercises. Grigorios Pavliotis is a Lecturer of Mathematics at Imperial College London. Andrew Stuart is a Professor of Mathematics at Warwick University. . 0aMathematics. 0aMathematical analysis. 0aAnalysis (Mathematics). 0aPartial differential equations. 0aComputer mathematics. 0aProbabilities. 0aPhysics. 0aApplied mathematics. 0aEngineering mathematics.14aMathematics.24aAnalysis.24aPartial Differential Equations.24aProbability Theory and Stochastic Processes.24aAppl.Mathematics/Computational Methods of Engineering.24aMathematical Methods in Physics.24aComputational Science and Engineering.1 aStuart, Andrew M.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387738284 0aTexts Applied in Mathematics,x0939-2475 ;v5340uhttp://dx.doi.org/10.1007/978-0-387-73829-1 aZDB-2-SMA c369644d369644 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK