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Mathematical Physics 1: Dynamical Systems and
Classical Mechanics (WS 2018/2019)


News
 [2019, January 25]

There will be a total number of 13 exercise sheets.
 [2018, December 16]

No tutorials on December 17.
You can hand in the homework to Kati Gabler, MA 873.
 [2018, December 06]

Exercise Sheet 07 is the last sheet counting for the first half of the semester.
 [2018, November 25]

No tutorials on November 26.
You can hand in the homework to Kati Gabler, MA 873.
The 6th exercise sheet only consists of two bonus exercises,
which may be used to collect extra points.
 [2018, November 22]

No office hours (Jan Techter) on November 22 and 29.
 [2018, November 15]

Sage notebooks from last tutorial:
discreteflows.ipynb,
smoothflows.ipynb,
desolve.ipynb
 [2018, November 4]

Office hour of Jan Techter changed to Thursday, 12:30  13:30.
 [2018, October 14]

First tutorials on October 22.
Exercise sheets
 Exercise Sheet 1 (Due Monday, October 29.)
 Exercise Sheet 2 (Due Monday, November 05.)
 Exercise Sheet 3 (Due Monday, November 12.)
 Exercise Sheet 4 (Due Monday, November 19.)
 Exercise Sheet 5 (Due Monday, November 26.)
 Exercise Sheet 6 (Due Monday, December 03.)
 Exercise Sheet 7 (Due Monday, December 10.)
 Exercise Sheet 8 (Due Monday, December 17.)
 Exercise Sheet 9 (Due Monday, January 7.)
 Exercise Sheet 10 (Due Monday, January 14.)
 Exercise Sheet 11 (Due Monday, January 21.)
 Exercise Sheet 12 (Due Monday, January 28.)
 Exercise Sheet 13 (Due Monday, February 04.)
Homework policy

To get a certificate for the tutorial you need to obtain an average grade of
60% on the homework assignments in both halves of the semester.

The homework assignments are to be handed in in groups of two people.

Homework assignments are due weekly.
They may be turned in at the beginning of the tutorial
or left in the letter box of Jan Techter (MA 873, Kati Gabler) before that time.

Justify each step of your computations.
Results without any explanation are not accepted.
Please write in a readable way.
Unreadable handwriting will not be corrected.
You may write your answers in English or German.
Contents
This is a course of the
Berlin Mathematical School
held in English.
I) Ordinary differential equations, Existence and uniqueness theorems, Dependence on initial conditions and parameters, Prolongation of solutions.
II) Dynamical systems, Flows and vector fields, Fixed points, Stability theorems, Linear dynamical systems, Linearization, Bifurcations, Normal forms of bifurcations, Attracting sets, Attractors.
III) Lagrangian mechanics in $\mathbb{R}^n$, Legendre Transformation, Hamiltonian mechanics in $\mathbb{R}^n$, Symplectic structure of the phase space, Poisson brackets, Canonical transformations, HamiltonJacobi theory, Symplectic integrators, Differentiable manifolds, Mechanics on manifolds, Symmetries and Noether theorem, Symplectic geometry, Poisson geometry, Rigid body equations of motion.
Literature
Office Hours
