Differential Equations, Dynamical Systems, and Linear Algebra
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This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.
Readership
Advanced undergraduate and graduate students studying mathematics.
Table of Contents
- Preface. First Examples. Newton's Equation and Kepler's Law. Linear Systems with Constant Coeffecients and Real Eigenvalues. Linear Systems with Constant Coefficients and Complex Eigenvalues. Linear Systems and Exponentials of Operators. Linear Systems and Canonical Forms of Operators. Contractions and Generic Properties of Operators. Fundamental Theory. Stability of Equilibria. Differential Equations for Electrical Circuits. The Poincare-Bendixson Theorem. Ecology. Periodic Attractors. Classical Mechanics. Nonautonomous Equations and Differentiability of Flows. Perturbation Theory and Structural Stability. Elementary Facts. Polynomials. On Canonical Forms. The Inverse Function Theorem. References. Answers to Selected Problems. Index.
Product details
- No. of pages: 358
- Language: English
- Copyright: © Academic Press 1974
- Published: April 28, 1974
- Imprint: Academic Press
- eBook ISBN: 9780080873763
About the Authors
Morris W. Hirsch
Affiliations and Expertise
University of Wisconsin, Madison, USA
Stephen Smale
Affiliations and Expertise
University of California, Berkeley, USA
Robert L. Devaney
Affiliations and Expertise
Boston University, MA, USA
Stephen Smale
Affiliations and Expertise
University of California, Berkeley, USA
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