Differential Equations, Dynamical Systems, and an Introduction to Chaos book cover

Differential Equations, Dynamical Systems, and an Introduction to Chaos

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.


Advanced Undergraduate and Graduate students studying mathematics, biology, chemistry, economics, physical sciences, physics, computer science and engineering

Hardbound, 432 Pages

Published: March 2012

Imprint: Academic Press

ISBN: 978-0-12-382010-5


  • 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


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