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OverviewThis book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we ``see'' how a mathematical pattern fits a physical problem is like ``hitting the ball.'' Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and phenomena, and the latter emphasizes geometric and physical insight. It will be useful for mathematicians and physicists learning singular perturbation analysis of ODE and PDE boundary value problems as well as the full range of related examples and problems. Prerequisites are basic skills in analysis and a good junior/senior level undergraduate course of mathematical physics. Full Product DetailsAuthor: John C. NeuPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.752kg ISBN: 9781470425555ISBN 10: 1470425556 Pages: 335 Publication Date: 30 November 2015 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsWhat is a singular perturbation? Asymptotic expansions Matched asymptotic expansions Matched asymptotic expansions in PDE Prandtl boundary layer theory Modulated oscillations Modulation theory by transforming variables Nonlinear resonance Bibliography IndexReviewsIn all, this book is a valuable completion to the literature on singular perturbations. It might be the first reference to read but also a good auxiliary in understanding more specialized books or papers. -Vladimir Rasvan, Zentralblatt MATH This is a lucid textbook written in an easy style. The book will be useful to researchers and graduate students in various areas of mathematics, mechanics, and physics. -V.A. Sobolev, Mathematical Reviews "In all, this book is a valuable completion to the literature on singular perturbations. It might be the first reference to read but also a good auxiliary in understanding more specialized books or papers."" —Vladimir Răsvan, Zentralblatt MATH ""This is a lucid textbook written in an easy style. The book will be useful to researchers and graduate students in various areas of mathematics, mechanics, and physics."" —V.A. Sobolev, Mathematical Reviews" Author InformationJohn C. Neu, University of California, Berkeley, CA, USA. Tab Content 6Author Website:Countries AvailableAll regions |
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