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Elsevier

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… Leer más

Descripción

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.

De interès para

Advanced undergraduate and graduate students studying mathematics.

Índice

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.

Detalles del producto

Sobre los autores

MH

Morris W. Hirsch

Morris W. Hirsch works at the University of Wisconsin, Madison, USA.
Afiliaciones y experiencia
University of Wisconsin, Madison, USA

RD

Robert L. Devaney

Robert L. Devaney works in the Department of Mathematics at Boston University, MA, USA.
Afiliaciones y experiencia
Department of Mathematics, Boston University, MA, USA

SS

Stephen Smale

Stephen Smale works in the Department of Mathematics at University of California, Berkeley, USA.
Afiliaciones y experiencia
Department of Mathematics, University of California, Berkeley, USA

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