**Graduate Studies in Mathematics**

Volume: 167;
2015;
326 pp;
Hardcover

MSC: Primary 34; 35; 37; 41; 76; 97;

Print ISBN: 978-1-4704-2555-5

Product Code: GSM/167

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-1-4704-2733-7
Product Code: GSM/167.E**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

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#### Supplemental Materials

# Singular Perturbation in the Physical Sciences

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*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
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.

#### Readership

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

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Singular Perturbation in the Physical Sciences

- Cover Cover11
- Title page iii4
- Contents v6
- Acknowledgment ix10
- Introduction xi12
- Chapter 1. What is a singular perturbation? 116
- Chapter 2. Asymptotic expansions 3146
- Chapter 3. Matched asymptotic expansions 7388
- Chapter 4. Matched asymptotic expansions in PDE 105120
- Chapter 5. Prandtl boundary layer theory 151166
- Chapter 6. Modulated oscillations 183198
- Chapter 7. Modulation theory by transforming variables 247262
- Chapter 8. Nonlinear resonance 287302
- Bibliography 319334
- Index 321336
- Back Cover Back Cover1346