**CDS 140a -- Fall 2009****First Term**

**Introduction to Dynamical Systems**

**Tuesdays and Thursdays****1 pm -2:30 pm****Location**: 214 Steele**Instructor**: Prof. Jerrold E. Marsden**Teaching Assistant**: Henry Jacobs

**Course Description**

*9 units (3-0-6); first term. Prerequisite: ACM 95 or equivalent*

Basic theory of dynamical systems in Euclidean space, including equilibria, stability, Lyapunov functions, periodic solutions, Poincaré–Bendixon theory, Poincaré maps. The Euler–Lagrange equations, mechanical systems, dissipation, energy as a Lyapunov function, and simple conservation laws. Introduction to basic bifurcations and eigenvalue crossing conditions. Discussion of bifurcations in applications, invariant manifolds, the method of averaging, Melnikov's method, and the Smale horseshoe.

## TA Sessions

will be held on Tuesday's at 4-5pm in 142 Keck. Office hours on Tuesdays 5-6pm and by appointment in Steele Rm 3 (in the basement).