Differential equations, dynamical systems, and linear algebra
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.
Read More ↓Title Statements
- Full title :Differential equations, dynamical systems, and linear algebra / Morris W. Hirsch and Stephen Smale.
Summary
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.
Read More ↓Edition Statements
- Publication Date:1974
Publication Statements
- Publisher(s):Academic Press
- Place of Publication:New York
- Language:eng
- Publication Date:1974
The Physical Object
- Description:1 online resource (xi, 358 pages) : : illustrations
Edition Identifiers
- ISBN:9780123495501, 0123495504, 9780080873763, 0080873766, 1281763624, 9781281763624
- oclc:ocn316566746
- LC Classification:QA3
- Dewey Decimal:515/.35
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.
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