Basic Information

• Instructor: Eugene Lerman
• e-mail: lerman at illinois edu
• Homepage: lerman.web.illinois.edu/
• Course page: lerman.web.illinois.edu/518/f23/518f23.html
• Office: 37 CAB
• Office Hours: see my calendar and/or by appointment
• Phone: 244-9510
• Class meets: MWF 11:00-11:50 am    in Davenport Hall 136
• Hand-written lecture notes will posted  here
• I plan to collect homework on Moodle (Moodle login help is here )

Prerequisites

A semester of graduate level differential geometry.  Familiarity with vector bundles a plus.

Course outline (tentative):

Symplectic linear algebra, canonical symplectic structure on the cotangent bundles, Darboux theorem, Lagrangian embedding theorem, Hamilton's principle and the Euler-Lagrange equations, Legendre transform, Poisson brackets, constants of motions, Lie group actions and moment maps, Marsden-Weinstein-Meyer reduction (aka symplectic quotients), rigid body dynamics, relative equilibria and their stability, completely integrable systems. 

Recommended Texts

• Lectures on symplectic geometry by Anna Cannas da Silva
• The Restricted Three-Body Problem and Holomorphic Curves by Urs Frauenfelder and Otto van Koert
• Introduction to Symplectic Topology  by Dusa McDuff and Dietmar Salamon (3d edition)

• Homework: Homework problems are to be assigned once a week. They are due the following week usually before midnight on Wednesdays. Late homework will be penalized. There are several reasons why I want the homework to be turned in on time. First of all, if you are not keeping up with the homework, you are not keeping up with the class, and then you may well get lost in the lectures. Secondly, it is hard to grade fairly the homework that is turned in late. The grader would have to keep careful track of the grading rubrics and so on. In short: late homework is bad for you and means more work for the grader.

  If you have questions about your homework score please take it up with the grader first. If you and the grader can't resolve the issue I will step in.

  If you have questions about the homework itself, please use the forum on Moodle and/or see me in the office hours.  If you email me with a question about homework I will likely post your question on Moodle and reply there.

• Grades: The course grade will be based on weekly homework (100%)

• Exams: no exams

Attendance is expected

Academic Integrity

Campus police safety information. Plus a one page handout

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Last modified: Tuesday, Aug 15, 2023