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Singular Perturbation in the Physical Sciences
John C. Neu, University of California, Berkeley, CA
Graduate Studies in Mathematics
2015; approx. 335 pp; hardcover
Volume: 167
ISBN-10: 1-4704-2555-6
ISBN-13: 978-1-4704-2555-5
List Price: US$79
Member Price: US$63.20
Order Code: GSM/167
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Not yet published.
Expected publication date is January 4, 2016.

This 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.

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Graduate students and researchers interested in asymptotic methods in mathematics and physics.

Table of Contents

  • What 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
  • Index
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