## Math 249 Mechanics Fall 2006

**Lecture notes** (PDF)

- Monday, September 25
- Wednesday, September 27
- Monday and Wednesday, October 2 and 4
- Derivation of Euler-Lagrange equations on Lie groups
- Canonical symplectic structure, October 16 and 18 (first part)
- Symplectic manifolds, October 23 (Exercises are as described in class, not in notes -- I recycled some old notes.)
- Hamilton's equations and Poisson brackets, October 25 (plus some proofs)
- Poisson brackets, October 30
- Quantization, and quantization on manifolds (November 6, 8, some of 13)
- Quantization of the rigid body, part 1 (November 22, some of 27)

**Homework**

**Optional supplemental readings**

*(really optional—some of this will
involve analytic or topological results, or applications, that I definitely
don't assume you all know or want to know)*

- Definitions and results for Lie groups, from
**Foundations of Mechanics**, Abraham and Marsden. The relevant material is indicated with a vertical
line in the left margin; the topological results, particularly those pertaining
to quotients, are far beyond what we'll need. I'll define in class, homework,
etc, any of this that we need.