000 04258nam a22005895i 4500
001 978-0-387-73829-1
003 DE-He213
005 20180115171416.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387738291
_9978-0-387-73829-1
024 7 _a10.1007/978-0-387-73829-1
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aPavliotis, Grigorios A.
_eauthor.
245 1 0 _aMultiscale Methods
_h[electronic resource] :
_bAveraging and Homogenization /
_cby Grigorios A. Pavliotis, Andrew M. Stuart.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _aXVIII, 310 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts Applied in Mathematics,
_x0939-2475 ;
_v53
505 0 _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.
520 _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. .
650 0 _aMathematics.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aPartial differential equations.
650 0 _aComputer mathematics.
650 0 _aProbabilities.
650 0 _aPhysics.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aPartial Differential Equations.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aComputational Science and Engineering.
700 1 _aStuart, Andrew M.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387738284
830 0 _aTexts Applied in Mathematics,
_x0939-2475 ;
_v53
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-73829-1
912 _aZDB-2-SMA
999 _c369644
_d369644