Differential Equations, Dynamical Systems, and an Introduction to Chaos

Informationen zum Autor Morris W. Hirsch works at the University of Wisconsin, Madison, USA. Stephen Smale works in the Department of Mathematics at University of California, Berkeley, USA. Robert L. Devaney works in the Department of Mathematics at Boston University, MA, USA. Klappentext A text by three of the world's most prominent mathematicians. Zusammenfassung Suitable for students in the fields of mathematics! science! and engineering! this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study. Inhaltsverzeichnis 1. First-Order Equations 2. Planar Linear Systems 3. Phase Portraits 4. Classification of Planar Systems 5. Higher Dimension Linear Algebra 6. Higher Dimension Linear Systems 7. Nonlinear Systems 8. Equilibria in Nonlinear Systems 9. Global Nonlinear Techniques 10. Closed Orbits and Limit Sets 11. Applications in Biology 12. Applications in Circuit Theory 13. Applications in Mechanics 14. The Lorenz System 15. Discrete Dynamical Systems 16. Homoclinic Phenomena 17. Existence and Uniqueness Revisited

Autorentext
Morris W. Hirsch works at the University of Wisconsin, Madison, USA. Stephen Smale works in the Department of Mathematics at University of California, Berkeley, USA.Robert L. Devaney works in the Department of Mathematics at Boston University, MA, USA.

Klappentext
A text by three of the world's most prominent mathematicians.

Zusammenfassung
Suitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.

Inhalt

1. First-Order Equations
   
   2. Planar Linear Systems
   3. Phase Portraits
   4. Classification of Planar Systems
   5. Higher Dimension Linear Algebra
   6. Higher Dimension Linear Systems
   7. Nonlinear Systems
   8. Equilibria in Nonlinear Systems
   9. Global Nonlinear Techniques
   10. Closed Orbits and Limit Sets
   11. Applications in Biology
   12. Applications in Circuit Theory
   13. Applications in Mechanics
   14. The Lorenz System
   15. Discrete Dynamical Systems
   16. Homoclinic Phenomena
   17. Existence and Uniqueness Revisited