Multiscale Methods : Averaging and Homogenization

Andrew Stuart

ISBN 10: 1441925325 / ISBN 13: 9781441925329

Verlag: Springer New York, Springer US, 2010

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9781441925329

Bibliografische Details

• Titel: Multiscale Methods : Averaging and Homogenization
• Verlag: Springer New York, Springer US
• Erscheinungsjahr: 2010
• Sprache: Englisch
• ISBN-10: 1441925325
• ISBN-13: 9781441925329
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 18 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 18 mm
• Gewicht: 499 Gramm

Über diesen Titel

Inhaltsangabe

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.

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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.