Multiscale Methods

1. Front Matter

   Pages I-XVIII

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 1-10

3. Background

   1. Front Matter

      Pages 11-11

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   2. Analysis

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 13-35

   3. Probability Theory and Stochastic Processes

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 37-57

   4. Ordinary Differential Equations

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 59-72

   5. Markov Chains

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 73-84

   6. Stochastic Differential Equations

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 85-101

   7. Partial Differential Equations

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 103-124

4. Perturbation Expansions

   1. Front Matter

      Pages 125-125

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   2. Invariant Manifolds for ODEs

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 127-135

   3. Averaging for Markov Chains

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 137-143

   4. Averaging for ODEs and SDEs

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 145-156

   5. Homogenization for ODEs and SDEs

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 157-182

   6. Homogenization for Elliptic PDEs

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 183-202

   7. Homogenization for Parabolic PDEs

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 203-226

   8. Averaging for Linear Transport and Parabolic PDEs

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 227-236

5. Theory

   1. Front Matter

      Pages 237-237

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   2. Invariant Manifolds for ODEs: The Convergence Theorem

      • Grigorios A. Pavliotis, Andrew M. Stuart

      Pages 239-244

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and s- bolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook - ries is to meet the current and future needs of these advances and to encourage the teaching of new couses. TAM will publish textbooks suitable for use in advanced undergraduate and - ginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research-level mo- graphs. Pasadena, California J.E. Marsden New York, New York L. Sirovich College Park, Maryland S.S. Antman To my parentsA????? and?o?????? and to my brother?????o. Carry Home.????o???. For my children Natalie, Sebastian, and Isobel.

• Averaging
• Computer-Aided Design (CAD)
• Homogenization
• Markov
• Methods
• Multiscale
• Pavliotis
• Probability theory
• Stuart
• calculus
• differential equation
• partial differential equation
• partial differential equations

From the reviews:

"The book is devoted to introduce problems in which different scales may appear. The value of the book is that a wide class of problems is presented and consequently different techniques used to attack these problems are shown. The book is divided in three different parts. … it can be used as a handbook for the arguements treated in the sequel." (Fabio Paronetto, Zentralblatt MATH, Vol. 1160, 2009)

• Department of Mathematics, Imperial College London, London, United Kingdom

  Grigorios A. Pavliotis

• Mathematics Institute, University of Warwick, Coventry, United Kingdom

  Andrew M. Stuart

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