| Softcover ISBN: | 978-0-8218-5269-9 |
| Product Code: | CLN/21 |
| List Price: | $35.00 |
| MAA Member Price: | $31.50 |
| AMS Member Price: | $28.00 |
| Electronic ISBN: | 978-1-4704-1764-2 |
| Product Code: | CLN/21.E |
| List Price: | $33.00 |
| MAA Member Price: | $29.70 |
| AMS Member Price: | $26.40 |
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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 one-semester 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.
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Table of Contents
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Averaging methods
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Chapter 1. Introduction to Part 1
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Chapter 2. Averaging differential equations
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Chapter 3. Difference equations
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Chapter 4. Averaging over random noise
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Boundary layer methods
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Chapter 5. Introduction to Part 2
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Chapter 6. Asymptotic stability and singular perturbations
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Chapter 7. QSSA for boundary layer problems
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Chapter 8. Other singular perturbation problems
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Appendix: Circuit theory
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Additional Material
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Reviews
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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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RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 one-semester 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
