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Mathematical Physics I: Dynamical Systems and Classical Mechanics (WS 13/14)
This is a course of the Berlin Mathematical School held in English.
Schedule
Lectures |
Prof. Dr. Yuri B. Suris |
Tue |
10:15 - 11:45 |
MA 749 |
Prof. Dr. Yuri B. Suris |
Thu |
10:15 - 11:45 |
MA 749 |
Tutorial |
Dr. Matteo Petrera |
Tue |
12:15 - 13:45 |
MA 749 |
Contents
Initial value problems, Dynamical systems, Stability theory,
Bifurcation theory, Lagrangian mechanics, Hamiltonian mechanics, Mechanics on smooth manifolds.
Literature
News
Last Tutorial on 04.02.14.
Last Homework will be Exercise Sheet 14 (Due: Tutorial on 04.02.14).
Remember that
to get the certificate for the tutorial (necessary condition for the oral exam)
you need to collect 60% of the total sum of points, i.e., 252 points
out of 14x30=420 points.
Homework sheets
Tutorial classes
- 22.10.13. IVPs, Existence and uniqueness of local solutions, Maximal solutions, Examples, Exercises.
- 29.10.13. Definition of dynamical system (continuous and discrete), Flows, Examples, Exercises.
- 05.11.13. Flows and vector fields, Lie series, Lie derivative of a function, Integrals of motion, Examples, Exercises.
- 12.11.13. Integrals of motion, Commuting flows, Stability of fixed points, Linear systems, Examples, Exercises.
- 19.11.13. Poincarè-Lyapunov theorem, Lyapunov functions, Examples, Exercises.
- 26.11.13. No Tutorial.
- 03.12.13. Non-autonoumous linear IVPs, Periodic linear IVPs, Examples, Exercises.
- 10.12.13. Stable, unstable and center manifolds, Examples, Exercises.
- 19.12.13. Mechanical systems, Conservative mechanical systems, Lagrangian mechanics, Examples, Exercises.
- 07.01.14. Euler-Lagrange equations, Symmetries of Lagrangians, Noether Theorem, Examples, Exercises.
- 14.01.14. Canonical Hamiltonian mechanics, canonical Hamilton equations, canonical Poisson brackets, Examples, Exercises.
- 21.01.14. Canonical and symplectic transformations, Examples, Exercises.
- 28.01.14. Smooth manifolds, motivations and some definitions, Examples, Exercises.
- 04.02.14. Vector fields and differential forms on manifolds, Examples, Exercises.
Homework policy
- To get a certificate for the tutorial you need to satisfactorily complete 60%
of the homework assignments.
- Homework assignments are due weekly. They may be turned in directly to Dr. Petrera at
the beginning of the Tuesday Tutorial (12:15)
or left in the letter box of Dr. Petrera (MA 701, Frau J. Downes)
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