MU03052 Geometric Methods in Physics I

Mathematical Institute in Opava
Winter 2011
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Introduction to the theory of certain geometric structures used in modern mathematical physics and their applications in the theory of Hamiltonian systems.
Syllabus
  • - 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)
Literature
    recommended literature
  • D. Krupka. Matematické základy OTR. info
  • P.J. Olver. Applications of Lie groups to differential equations. 1993. info
  • M. Nakahara. Geometry, Topology and Physics. Institute of Physics Publishing, 1990. info
  • V.I. Arnol'd. Mathematical Methods of Classical Mechanics. Springer, 1989. info
    not specified
  • O. Krupková. The Geometry of Variational ODE. Lecture Notes in Mathematics 1678, Springer, 1997. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The requirements for the final test (Pre-Exam Credit) are to be specified by the tutorial lecturer upon agreement of the lecturer.
The course is also listed under the following terms Winter 1997, Summer 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2011, recent)
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