Differential Equations, Dynamical Systems, and Linear Algebra

By

  • Morris Hirsch, University of Wisconsin, Madison, USA
  • Stephen Smale, University of California, Berkeley, USA

Audience

Advanced undergraduate and graduate students studying mathematics.

 

Book information

  • Published: April 1974
  • Imprint: ACADEMIC PRESS
  • ISBN: 978-0-12-349550-1


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.