| Ambitious Plan for Physics 200B |
| Hamiltonian Mechanics |
| Hamilton’s equations (review), canonical transformations, symplectic structure, generating functions, Hamilton-Jacobi theory in several variables, separation of variables, integrability, action-angle variables, librations and rotations, invariant tori, canonical perturbation theory, resonances and their removal, KAM theorem |
| Nonlinear Dynamics and Chaos |
| Nonlinear oscillators, Poincare-Lindstedt method, multiple time scale method, relaxation oscillations, maps, Lyapunov exponents, chaos and KAM tori, strongly chaotic systems, period doubling cascade, intermittency |
| Ergodicity and the Approach to Equilibrium |
| Master equation, equilibrium, detailed balance, H-theorem, recurrence, ergodicity, mixing, Boltzmann equation, transport phenomena, Onsager reciprocity |
| Miscellaneous |
| Grading |
There will be seven problem sets, one midterm, and a comprehensive final. Roughly, I will use the following formula to determine grades: 40% HW, 50% final, 10% intangibles. I expect your homework to be neat, legible, with multiple pages stapled. Failure to meet these expectations could result in tragic consequences. |