**Graduate Studies in Mathematics**

Volume: 140;
2012;
356 pp;
Hardcover

MSC: Primary 34; 37;

Print ISBN: 978-0-8218-8328-0

Product Code: GSM/140

List Price: $64.00

Individual Member Price: $51.20

**Electronic ISBN: 978-0-8218-9104-9
Product Code: GSM/140.E**

List Price: $64.00

Individual Member Price: $51.20

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#### Supplemental Materials

# Ordinary Differential Equations and Dynamical Systems

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*Gerald Teschl*

This book provides a self-contained introduction to ordinary
differential equations and dynamical systems suitable for beginning
graduate students.

The first part begins with some simple examples of explicitly
solvable equations and a first glance at qualitative methods. Then the
fundamental results concerning the initial value problem are proved:
existence, uniqueness, extensibility, dependence on initial
conditions. Furthermore, linear equations are considered, including
the Floquet theorem, and some perturbation results. As somewhat
independent topics, the Frobenius method for linear equations in the
complex domain is established and Sturm–Liouville boundary value
problems, including oscillation theory, are investigated.

The second part introduces the concept of a dynamical system. The
Poincaré–Bendixson theorem is proved, and several
examples of planar systems from classical mechanics, ecology, and
electrical engineering are investigated. Moreover, attractors,
Hamiltonian systems, the KAM theorem, and periodic solutions are
discussed. Finally, stability is studied, including the stable
manifold and the Hartman–Grobman theorem for both continuous and
discrete systems.

The third part introduces chaos, beginning with the basics for
iterated interval maps and ending with the Smale–Birkhoff theorem and
the Melnikov method for homoclinic orbits.

The text contains almost three hundred exercises. Additionally,
the use of mathematical software systems is incorporated throughout,
showing how they can help in the study of differential equations.

#### Table of Contents

# Table of Contents

## Ordinary Differential Equations and Dynamical Systems

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface ix10 free
- Chapter 1. Introduction 316
- Chapter 2. Initial value problems 3346
- Chapter 3. Linear equations 5972
- Chapter 4. Differential equations in the complex domain 111124
- Chapter 5. Boundary value problems 141154
- Chapter 6. Dynamical systems 187200
- Chapter 7. Planar dynamical systems 209222
- Chapter 8. Higher dimensional dynamical systems 229242
- Chapter 9. Local behavior near fixed points 255268
- Chapter 10. Discrete dynamical systems 281294
- Chapter 11. Discrete dynamical systems in one dimension 293306
- Chapter 12. Periodic solutions 317330
- Chapter 13. Chaos in higher dimensional systems 333346
- Bibliographical notes 341354
- Bibliography 345358
- Glossary of notation 349362
- Index 351364 free
- Back Cover Back Cover1370

#### Readership

Graduate students interested in ordinary differential equations and dynamical systems.

#### Reviews

It's easy to build all sorts of courses from this book — a classical one-semester course with a brief introduction to dynamical systems, a one-semester dynamical systems course with just brief coverage of the existence and linear systems theory, or a rather nice two-semester course based on most (if not all) of the material.

-- MAA Reviews