Course: Geometric Methods in Physics I

» List of faculties » MU » MU
Course title Geometric Methods in Physics I
Course code MU/03052
Organizational form of instruction Lecture + Lesson
Level of course not specified
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
Course content
- Basic differential geometry (manifolds, definition and basic properties of vector fields and differential forms and operations over them) - Hamiltonian systems (the Poisson structures and their properties, the Darboux theorem, Hamiltonian, the Hamilton equations, integrals of motion, complete integrability and the Liouville theorem, bihamiltonian systems) - The Hamilton-Jacobi theory and related issues (complete integral, the Jacobi integration method, the Hamilton--Jacobi equation, separation of variables, the action-angle variables)

Learning activities and teaching methods
Recommended literature
  • D. Krupka. Matematické základy OTR.
  • M. Nakahara. Geometry, Topology and Physics. Institute of Physics Publishing, 1990.
  • O. Krupková. The Geometry of Variational ODE. Lecture Notes in Mathematics 1678, Springer, 1997.
  • P.J. Olver. Applications of Lie groups to differential equations. 1993.
  • V.I. Arnol'd. Mathematical Methods of Classical Mechanics. Springer, 1989.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester