000  04258nam a22005895i 4500  

001  9780387738291  
003  DEHe213  
005  20180115171416.0  
007  cr nn 008mamaa  
008  100301s2008 xxu s  0eng d  
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_a9780387738291 _99780387738291 

024  7 
_a10.1007/9780387738291 _2doi 

050  4  _aQA299.6433  
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, _x09392475 ; _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 twentyone 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, _x09392475 ; _v53 

856  4  0  _uhttp://dx.doi.org/10.1007/9780387738291 
912  _aZDB2SMA  
999 
_c369644 _d369644 