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Differential Dynamical Systems

Part of Monographs on Mathematical Modeling and Computation

Author: James D. Meiss, University of Colorado, Boulder

Date Published: January 2008
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Paperback
isbn: 9780898716351

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Description

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines traditional teaching on ordinary differential equations with an introduction to the more modern theory of dynamical systems, placing this theory in the context of applications to physics, biology, chemistry, and engineering. Beginning with linear systems, including matrix algebra, the focus then shifts to foundational material on non-linear differential equations, drawing heavily on the contraction mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts - flow, chaos, invariant manifolds, bifurcation, etc. An appendix provides simple codes written in Maple®, Mathematica®, and MATLAB® software to give students practice with computation applied to dynamical systems problems. For senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with differential equations and linear algebra and have had some exposure to advanced calculus.
- Combines a traditional theoretical development of ordinary differential equations with a modern dynamical systems viewpoint and an emphasis on applications
- Provides a broad perspective on the development of invariant manifolds, bifurcation theory, chaos and geometric Hamiltonian dynamics
- Exercises and examples include applications to biological, electronic, mechanical, fluid, plasma and chemical dynamics
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Product details
- Date Published: January 2008
- format: Paperback
- isbn: 9780898716351
- length: 436 pages
- dimensions: 254 x 174 x 23 mm
- weight: 0.754kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface
List of figures
List of tables
1. Introduction
2. Linear systems
3. Existence and uniqueness
4. Dynamical systems
5. Invariant manifolds
6. The phase plane
7. Chaotic dynamics
8. Bifurcation theory
9. Hamiltonian dynamics
A. Mathematical software
Bibliography
Index.
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Differential Dynamical Systems

James D. Meiss
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Author
James D. Meiss, University of Colorado, Boulder
James D. Meiss is a Professor in the Department of Applied Mathematics at the University of Colorado at Boulder. He is a fellow of the American Physical Society.