Differential Equations – Morris W. Hirsch – 2nd Edition

Description

Thirty years in the making, this revised text by three of the world’s leading mathematicians covers the dynamical aspects of ordinary . it explores the relations between and certain fields outside pure mathematics, and has become the standard for graduate courses in this area. The Second Edition now brings to the brink of contemporary research, starting from a background that includes only and elementary linear algebra.

The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field’s Medal for his work in dynamical systems.

* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon

NEW IN THIS EDITION

* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil’nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems

Table of Content


1. First Order Equations
2. Planar Linear Systems
3. Phase Portraits
4. Classification of Planar Systems
5. Higher Dimensional Linear Algebra
6. Higher Dimensional Linear Systems
7. Fundamental Theory
8. Equilibria in Nonlinear Systems
9. 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. Applications in Other Fields
16. Homoclinic Phenomana
17. Discrete Dynamical Systems
18. Higher Dimensional Discrete Systems.

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