Fakultät II
Institut für Mathematik

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

 Lectures Tutorials Prof. Dr. Yuri B. Suris Tuesday 12 - 14 MA 749 Thursday 10 - 12 MA 749 Jan Techter Monday 10 - 12 MA 750 Monday 14 - 16 MA 642

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: discrete-flows.ipynb, smooth-flows.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.

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, Hamilton-Jacobi theory, Symplectic integrators, Differentiable manifolds, Mechanics on manifolds, Symmetries and Noether theorem, Symplectic geometry, Poisson geometry, Rigid body equations of motion.

Office Hours

 Prof. Dr. Yuri B. Suris Jan Techter Wednesday 14-15 MA 827 Thursday 12:30-13:30 MA 883

 Jan Techter . 25.01.2019.