CDS 140a -- Fall 2007
Introduction to Dynamics
Prerequisites: ACM 95 or equivalent
Basics in topics in dynamics 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.
Instructor
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Aaron D. Ames
ames@cds.caltech.edu
Steele 3, x3366
Office hours: TBA
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Sujit Nair
nair@cds.caltech.edu
Steele 5, x3367
Office hours: TBA
Lectures
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T & Th 10:30am-noon; Steele 214
Course Announcements
- The first lecture will be held on Tuesday, October 2 in Steele 214.
Course Policy
- Homework assignments will be handed out every second or third lecture and will be due in class one week later. Homework extensions will be given under special circumstances: You should contact me in advance to request an extension. No late homeworks will be otherwise accepted.
- There will be a midterm (tentatively scheduled for Tuesday November 6) and a final exam.
- Your homeworks, midterm and final exams will contribute to 45%, 25% and 30% of your final grade, respectively.
Textbooks
- Ferdinand Verhulst, Nonlinear Differential Equations and Dynamical Systems, Second Edition (available in the bookstore).
Syllabus (Tentative)
Homework Assignments