DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS PDF

PDF Ordinary Differential Equations and Dynamical Systems

Linear dynamical systems can be solved in terms of simple functions and the behavior of all orbits classified. In a linear system the phase space is the N-dimensional Euclidean space, so any point in phase space can be represented by a vector with N numbers. The analysis of linear systems is possible because they satisfy a superposition principle: if u(t) and w(t) satisfy the differential ...

Differential Equations, Dynamical Systems, and Linear Algebra

Differential Equations, Dynamical Systems, and Linear Algebra •MORRIS W. HIRSCH AND STEPHEN SM ALE University of California, Berkeley /PI ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers San Diego New York Boston London Sydney Tokyo Toronto . Contents Preface CHAPTER1 FIRST EXAMPLES 1. The Simplest Examples 2. Linear Systems with Constant CoeflScients Notes 1 9 13 CHAPTER 2 NEWTON ...