Multiscale Methods - Stuart, Andrew

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Résumé :
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.

Sommaire:
The author of this book is one of the leading world experts on multiscale methods, a hot area in applied mathematics. The book is meant to be an introduction, aimed primarily towards graduate students. Part I of the book and Part III of the book are necessarily terse and present the wide range of applications of the ideas, and illustrate their unity. The 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....