MU03052 Geometric Methods in Physics I

Mathematical Institute in Opava
Winter 2007
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Guaranteed by
doc. RNDr. Kristína Smítalová, CSc.
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 (in Czech)
Základní orientace v moderních geometrických modelech fyzikálních teorií.
Syllabus (in Czech)
  • - Fibrované prostory a jejich yetová prodloužení (surjektivní submerze, prolongace fibrované variety, horizontální a kontaltní formy, projektabilní vektorová pole a jejich prodloužení)
    - Lagrangeovy systémy (Lagrangián na fibrované varietě, funkce akce, první variační formule, Eulerova-Lagrangeova forma, extremály)
    - Hamiltonovy systémy (Lepageova forma, rozšířený Lagrangián, Hamiltonovy rovnice, regularita, Legendreova transformace)
    - Symetrie Lagrangeových struktur (symetrie Lagrangiánu a Eulerovy-Lagrangeovy formy, teorém Noetherové, použití symetrií v mechanice)
    - Hamiltonova-Jacobiho teorie (pole extremál, úplný integrál, Jacobiho integrační metoda)
Literature
    recommended literature
  • D. Krupka. Matematické základy OTR. info
  • O. Krupková. The Geometry of Variational ODE. Lecture Notes in Mathematics 1678, Springer, 1997. info
  • M. Nakahara. Geometry, Topology and Physics. Institute of Physics Publishing, 1990. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
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 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2007, recent)
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