Differential Equations, Dynamical Systems, and an Introduction to Chaos / Morris W. Hirsch, Stephen Smale, Robert L. Devaney.

Includes bibliographical references (pages 411-413) and index.

1. First-Order Equations -- 2. Planar Linear Systems -- 3. Phase Portraits for Planar Systems -- 4. Classification of Planar Systems -- 5. Higher-Dimensional Linear Algebra -- 6. Higher-Dimensional 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.

"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. Classic text by three of the world's most prominent mathematicians. Continues the tradition of expository excellence. Contains updated material and expanded applications for use in applied studies."--Publisher's description.