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Hardcover ISBN:  9781470425555 
Product Code:  GSM/167 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Sale Price:  $87.75 
eBook ISBN:  9781470427337 
Product Code:  GSM/167.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Sale Price:  $55.25 
Hardcover ISBN:  9781470425555 
eBook ISBN:  9781470427337 
Product Code:  GSM/167.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Sale Price:  $143.00 $115.38 

Book DetailsGraduate Studies in MathematicsVolume: 167; 2015; 326 ppMSC: Primary 34; 35; 37; 41; 76; 97
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 followthrough. 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.
ReadershipGraduate students and researchers interested in asymptotic methods in mathematics and physics.

Table of Contents

Chapters

Chapter 1. What is a singular perturbation?

Chapter 2. Asymptotic expansions

Chapter 3. Matched asymptotic expansions

Chapter 4. Matched asymptotic expansions in PDE

Chapter 5. Prandtl boundary layer theory

Chapter 6. Modulated oscillations

Chapter 7. Modulation theory by transforming variables

Chapter 8. Nonlinear resonance


Additional Material

Reviews

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


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

Chapters

Chapter 1. What is a singular perturbation?

Chapter 2. Asymptotic expansions

Chapter 3. Matched asymptotic expansions

Chapter 4. Matched asymptotic expansions in PDE

Chapter 5. Prandtl boundary layer theory

Chapter 6. Modulated oscillations

Chapter 7. Modulation theory by transforming variables

Chapter 8. Nonlinear resonance

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