Softcover ISBN:  9780821852699 
Product Code:  CLN/21 
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Electronic ISBN:  9781470417642 
Product Code:  CLN/21.E 
List Price:  $33.00 
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Book DetailsCourant Lecture NotesVolume: 21; 2010; 163 ppMSC: Primary 34; 37; 39; 45; 60; 92;
This book is based on a course on advanced topics in differential equations given in Spring 2010 at the Courant Institute of Mathematical Sciences. It describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the mathematical sciences and engineering that involve singular perturbations. There is a large literature devoted to singular perturbation methods for ordinary and partial differential equations, but there are not many studies that deal with difference equations, Volterra integral equations, and purely nonlinear gradient systems where there is no dominant linear part. Designed for a onesemester course for students in applied mathematics, it is the purpose of this book to present sufficient rigorous methods and examples to position the reader to investigate singular perturbation problems in such equations.
ReadershipGraduate students interested in singular perturbation methods.

Table of Contents

Averaging methods

Chapter 1. Introduction to Part 1

Chapter 2. Averaging differential equations

Chapter 3. Difference equations

Chapter 4. Averaging over random noise

Boundary layer methods

Chapter 5. Introduction to Part 2

Chapter 6. Asymptotic stability and singular perturbations

Chapter 7. QSSA for boundary layer problems

Chapter 8. Other singular perturbation problems

Appendix: Circuit theory


Additional Material

Reviews

The topic of this book is well focused...Many examples are covered...ranging from mechanics to chemical reactions, electronics, neurosciences, etc. ...the text is well written.
Eric Benoît, Mathematical Reviews


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 Book Details
 Table of Contents
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This book is based on a course on advanced topics in differential equations given in Spring 2010 at the Courant Institute of Mathematical Sciences. It describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the mathematical sciences and engineering that involve singular perturbations. There is a large literature devoted to singular perturbation methods for ordinary and partial differential equations, but there are not many studies that deal with difference equations, Volterra integral equations, and purely nonlinear gradient systems where there is no dominant linear part. Designed for a onesemester course for students in applied mathematics, it is the purpose of this book to present sufficient rigorous methods and examples to position the reader to investigate singular perturbation problems in such equations.
Graduate students interested in singular perturbation methods.

Averaging methods

Chapter 1. Introduction to Part 1

Chapter 2. Averaging differential equations

Chapter 3. Difference equations

Chapter 4. Averaging over random noise

Boundary layer methods

Chapter 5. Introduction to Part 2

Chapter 6. Asymptotic stability and singular perturbations

Chapter 7. QSSA for boundary layer problems

Chapter 8. Other singular perturbation problems

Appendix: Circuit theory

The topic of this book is well focused...Many examples are covered...ranging from mechanics to chemical reactions, electronics, neurosciences, etc. ...the text is well written.
Eric Benoît, Mathematical Reviews