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The Resource Multiscale Methods : Averaging and Homogenization, by Grigoris Pavliotis, Andrew Stuart, (electronic resource)
Multiscale Methods : Averaging and Homogenization, by Grigoris Pavliotis, Andrew Stuart, (electronic resource)
Resource Information
The item Multiscale Methods : Averaging and Homogenization, by Grigoris Pavliotis, Andrew Stuart, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Multiscale Methods : Averaging and Homogenization, by Grigoris Pavliotis, Andrew Stuart, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This 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.
 Language

 eng
 eng
 Edition
 1st ed. 2008.
 Extent
 1 online resource (313 p.)
 Note
 Description based upon print version of record
 Contents

 Background
 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
 Isbn
 9780387738291
 Label
 Multiscale Methods : Averaging and Homogenization
 Title
 Multiscale Methods
 Title remainder
 Averaging and Homogenization
 Statement of responsibility
 by Grigoris Pavliotis, Andrew Stuart
 Subject

 Computer mathematics
 Engineering mathematics
 Mathematical Methods in Physics
 Mathematical analysis
 Mathematical and Computational Engineering
 Partial Differential Equations
 Partial differential equations
 Analysis
 Probabilities
 Probability Theory and Stochastic Processes
 Physics
 Analysis (Mathematics)
 Applied mathematics
 Computational Science and Engineering
 Language

 eng
 eng
 Summary
 This 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.
 http://library.link/vocab/creatorName
 Pavliotis, Grigoris
 Dewey number
 515.35
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 gwV2t0ujTc
 YYi4g6T2A4
 Language note
 English
 LC call number
 QA299.6433
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Stuart, Andrew.
 Series statement
 Texts in Applied Mathematics,
 http://library.link/vocab/subjectName

 Mathematical analysis
 Analysis (Mathematics)
 Partial differential equations
 Probabilities
 Applied mathematics
 Engineering mathematics
 Physics
 Computer mathematics
 Analysis
 Partial Differential Equations
 Probability Theory and Stochastic Processes
 Mathematical and Computational Engineering
 Mathematical Methods in Physics
 Computational Science and Engineering
 Label
 Multiscale Methods : Averaging and Homogenization, by Grigoris Pavliotis, Andrew Stuart, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Background  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
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (313 p.)
 Form of item
 online
 Isbn
 9780387738291
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780387738291
 Specific material designation
 remote
 System control number

 (CKB)1000000000492068
 (EBL)3062899
 (SSID)ssj0000319094
 (PQKBManifestationID)11265722
 (PQKBTitleCode)TC0000319094
 (PQKBWorkID)10336595
 (PQKB)11665495
 (DEHe213)9780387738291
 (MiAaPQ)EBC3062899
 (EXLCZ)991000000000492068
 Label
 Multiscale Methods : Averaging and Homogenization, by Grigoris Pavliotis, Andrew Stuart, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Background  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
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (313 p.)
 Form of item
 online
 Isbn
 9780387738291
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780387738291
 Specific material designation
 remote
 System control number

 (CKB)1000000000492068
 (EBL)3062899
 (SSID)ssj0000319094
 (PQKBManifestationID)11265722
 (PQKBTitleCode)TC0000319094
 (PQKBWorkID)10336595
 (PQKB)11665495
 (DEHe213)9780387738291
 (MiAaPQ)EBC3062899
 (EXLCZ)991000000000492068
Subject
 Computer mathematics
 Engineering mathematics
 Mathematical Methods in Physics
 Mathematical analysis
 Mathematical and Computational Engineering
 Partial Differential Equations
 Partial differential equations
 Analysis
 Probabilities
 Probability Theory and Stochastic Processes
 Physics
 Analysis (Mathematics)
 Applied mathematics
 Computational Science and Engineering
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