Singular Perturbation in the Physical SciencesShare this page
John C. Neu
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
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.
Table of Contents
Table of Contents
Singular Perturbation in the Physical Sciences
Graduate students and researchers interested in asymptotic methods in mathematics and physics.
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