Arbeitsgruppe Geometrie

Mathematical Physics I  (WS 2014/15)

Schedule

This is a course of the Berlin Mathematical School held in English.

Office hours

Contents

• Ordinary differential equations, existence and uniqueness theorems, dependence on initial conditions and parameters, prolongation of solutions.

• Dynamical systems, flows and vector fields, fixed points, stability theorems, linear dynamical systems, linearization, bifurcations, normal forms of bifurcations, attracting sets, attractors.

• Lagrangian mechanics in R^n, Legendre transformation, Hamiltonian mechanics in 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

Literature

• M. Petrera. Mathematical Physics I: Dynamical Systems and Classical Mechanics. Lecture Notes. 2013, Logos Verlag Berlin. ISBN: 978-3-8325-3569-8

News

• You may pick up your certificates from our secretary Ms Jean Downes (MA 701). Please consider the office hours!

Homework sheets

Homework policy

• Homework assignments are due weekly at the beginning of the Tutorial (Tuesday, 12:15). They have to be turned in directly to the lecturer. No homework will be accepted after the deadline has passed.

• Homework assignments can be solved in groups of two people.

• To get the Übungsschein, you need to satisfactorily complete 60% of the homework assignments.

Handwritten manuscript