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Differential Equations, Dynamical Systems, and Linear Algebra

  • 1st Edition - April 28, 1974
  • Newer edition is available
  • Authors: Morris W. Hirsch, Robert L. Devaney, Stephen Smale
  • Language: English

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… Read more

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Description

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

About the authors

MH

Morris W. Hirsch

Morris W. Hirsch works at the University of Wisconsin, Madison, USA.
Affiliations and expertise
University of Wisconsin, Madison, USA

RD

Robert L. Devaney

Robert L. Devaney works in the Department of Mathematics at Boston University, MA, USA.
Affiliations and expertise
Department of Mathematics, Boston University, MA, USA

SS

Stephen Smale

Stephen Smale works in the Department of Mathematics at University of California, Berkeley, USA.
Affiliations and expertise
Department of Mathematics, University of California, Berkeley, USA

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