Differential Equations, Dynamical Systems, and an Introduction to Chaos

3. Auflage 2012
ISBN: 978-0-12-382010-5
Verlag: Elsevier Science Publishing Co Inc

Buch, Englisch, 432 Seiten, Format (B × H): 158 mm x 236 mm, Gewicht: 780 g

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.

Zielgruppe

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

Autoren/Hrsg.

Hirsch, Morris W.

Devaney, Robert L.

Smale, Stephen

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

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

Über Autor(innen)

Devaney, Robert L.
Robert L. Devaney works in the Department of Mathematics at Boston University, MA, USA.

Hirsch, Morris W.
Morris W. Hirsch works at the University of Wisconsin, Madison, USA.

Smale, Stephen
Stephen Smale works in the Department of Mathematics at University of California, Berkeley, USA.