**Courant Lecture Notes**

Volume: 21;
2010;
163 pp;
Softcover

MSC: Primary 34; 37; 39; 45; 60; 92;

Print ISBN: 978-0-8218-5269-9

Product Code: CLN/21

List Price: $33.00

Individual Member Price: $26.40

**Electronic ISBN: 978-1-4704-1764-2
Product Code: CLN/21.E**

List Price: $33.00

Individual Member Price: $26.40

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#### Supplemental Materials

# Quasi-Static State Analysis of Differential, Difference, Integral, and Gradient Systems

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*Frank C. Hoppensteadt*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

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.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Readership

Graduate students interested in singular perturbation methods.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Quasi-Static State Analysis of Differential, Difference, Integral, and Gradient Systems

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Part I. Averaging methods 116
- Introduction to Part 1 318
- Averaging differential equations 924
- Difference equations 4964
- Averaging over random noise 6782
- Part II. Boundary layer methods 8398
- Introduction to Part 2 85100
- Asymptotic stability and singular perturbations 89104
- QSSA for boundary layer problems 105120
- Other singular perturbation problems 129144
- Appendix: Circuit theory 155170
- Bibliography 159174
- Index 161176
- Back Cover Back Cover1182