Bibliothèque de L'IMIST/CNRST

Includes bibliographical references and index.

Introduction -- pt. 1. Background -- Analysis -- Probability theory and stochastic processes -- Ordinary differential equations -- Markov chains -- Stochasitc differential equations -- Partial differential equations -- pt. II. 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 -- Invariant manifolds for ODEs: 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.

"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.