# Multiscale Methods

## Averaging and Homogenization

Part of the Texts Applied in Mathematics book series (TAM, volume 53)

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Textbook

Part of the Texts Applied in Mathematics book series (TAM, volume 53)

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 twenty-one 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.

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

- DOI https://doi.org/10.1007/978-0-387-73829-1
- Copyright Information Springer Science+Business Media, LLC 2008
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-387-73828-4
- Online ISBN 978-0-387-73829-1
- Series Print ISSN 0939-2475
- Buy this book on publisher's site