Differential Equations, Dynamical Systems, and an Introduction to Chaos

This classic book presents the mathematical rigor, theory, and applications needed to understand dynamical systems in an attempt to solve problems in engineering, science, and biology

Morris W. Hirsch (Author), Stephen Smale (Author), Robert L. Devaney (Author)

9780123820105, Elsevier Science

Hardback, published 26 April 2012

432 pages
22.9 x 15.1 x 2.8 cm, 0.79 kg

Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.

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

Subject Areas: Applied mathematics [PBW], Differential calculus & equations [PBKJ]