Polyteknisk Boghandel

The book is meant to be an introduction, aimed primarily towards graduate students. Part I of the book (theoretical foundations) and Part III of the book (proving theorems concerning simplified versions of the models that are studied in Part II) are necessarily terse and present the wide range of applications of the ideas, and illustrate their unity. The subject matter in these set of notes has, for the most part, been known for several decades. However, the particular presentation of the material here is particularly suited to the pedagogical goal of communicating the subject area to the wide range of mathematicians, scientists and engineers who are currently engaged in the use of these tools to tackle the enormous range of applications that require them. Extensions and generalizations of the results presented in these notes, as well as references to the literature, are given in the Discussion and Bibliography section, at the end of each chapter. With the exception of Chapter 1, all chapters are supplemented with exercises.

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.