MU:MU03052 Geometric Methods in Phys. I - Course Information
MU03052 Geometric Methods in Physics I
Mathematical Institute in OpavaWinter 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
- Geometry (programme MU, M1101)
- Geometry (programme MU, N1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematical Analysis (programme MU, N1101)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Secondary School Teacher Training in Mathematics (programme FPF, M7504)
- 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)
- - Basic differential geometry (manifolds, definition and basic properties of vector fields and differential forms and operations over them)
- 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.
- Enrolment Statistics (Winter 2011, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2011/MU03052