Differential Equations, Dynamical Systems, and an Introduction to Chaos

✍ Scribed by Devaney, Robert L.;Hirsch, Morris W.;Smale, Stephen

• Publisher: Elsevier Science;Academic Press
• Year: 2013;2012
• Tongue: English
• Edition: 3rd edition
• Category: Library

✦ Synopsis

Chapter 1 First-order equations -- chapter 2 Planar linear systems -- chapter 3 Phase portraits for planar systems -- chapter 4 Classification on planar systems -- chapter 5 Higher-dimensional linear algebra -- chapter 6 Higher-dimensional linear systems -- chapter 7 Nonlinear systems -- chapter 8 Equilibria in nonlinear systems -- chapter 9 Global nonlinear techniques -- chapter 10 Closed orbits and limit sets -- chapter 11 Applications in biology -- chapter 12 Applications in circuit theory -- chapter 13 Applications in mechanics -- chapter 14 The Lorenz system -- chapter 15 Discrete dynamical systems -- chapter 16 Homoclinic phenomena -- chapter 17 Existence and uniqueness revisited.;"Differential Equations, Dynamical Systems, and an Introduction to Chaos, now in its third edition, covers the dynamical aspects of ordinary differential equations. It explores the relations between dynamical systems and certain fields outside pure mathematics, and continues to be the standard textbook for advanced undergraduate and graduate courses in this area.""Written for students with a background in calculus and elementary linear algebra, the text is rigorous yet accessible and contains examples and explorations to reinforce learning."--Back cover.

✦ Table of Contents

Chapter 1 First-order equations --
chapter 2 Planar linear systems --
chapter 3 Phase portraits for planar systems --
chapter 4 Classification on planar systems --
chapter 5 Higher-dimensional linear algebra --
chapter 6 Higher-dimensional linear systems --
chapter 7 Nonlinear systems --
chapter 8 Equilibria in nonlinear systems --
chapter 9 Global nonlinear techniques --
chapter 10 Closed orbits and limit sets --
chapter 11 Applications in biology --
chapter 12 Applications in circuit theory --
chapter 13 Applications in mechanics --
chapter 14 The Lorenz system --
chapter 15 Discrete dynamical systems --
chapter 16 Homoclinic phenomena --
chapter 17 Existence and uniqueness revisited.

✦ Subjects

Algebras, Linear;Algèbre linéaire;Chaos (théorie des systèmes);Chaostheorie;Chaotic behavior in systems;Chaotisches System;Differential equations;Differentialekvationer;Differentialgleichung;Dynamisches System;Équations différentielles;Linjär algebra;mathematics;Systèmes dynamiques;Electronic books;Équations différentielles;Algèbre linéaire;Systèmes dynamiques;Chaos (théorie des systèmes);Linjär algebra