Description 
1 online resource (xviii, 307 pages) : illustrations 
Series 
Texts in applied mathematics ; 53 

Texts in applied mathematics ; 53

Contents 
Introduction  Analysis  Probability Theory and Stochastic Processes  Ordinary Differential Equations  Markov Chains  Stochastic Differential Equations  Partial Differential Equations  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  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 Parabolic PDEs: The Convergence Theorem  Averaging for Linear Transport and Parabolic PDEs: The Convergence Theorem 
Summary 
"This introduction to multiscale methods gives readers a broad overview of their many uses and applications. 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 solve 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. With the exception of Chapter One, all of the 21 chapters are supplemented with exercises."Jacket 
Bibliography 
Includes bibliographical references and index 
Notes 
Print version record 
Subject 
Differential equations.


Differential equations, Partial.

Form 
Electronic book

Author 
Stuart, A. M.

LC no. 
2007941385 
ISBN 
0387738282 (hbk.) 

0387738290 

9780387738284 (hbk.) 

9780387738291 
