MU03265 Variational Analysis on Manifolds

Mathematical Institute in Opava
Summer 2009
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
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)
Metody hledání extrémů funkcionálů na varietách vhodných vlastností. Moderní postupy variačního počtu.
Syllabus (in Czech)
  • - Jety diferencovatelných zobrazení, fibrované variety a jejich prodloužení, variety kontaktních elementů
    - Lagrangeovy struktury (horizontální a kontaktní formy, Lepageovy formy, první variační formule, Eulerovy-Lagrangeovy rovnice, Hamiltonovy rovnice)
    - Symetrie Lagrangeových struktur (transformace invariance Lagrangeovy struktury, zobecněná transformace invariance, první teorém Noetherové, přirozené Lagrangeovy struktury, druhý teorém Noetherové)
    - Pole extremál a Hamiltonova-Jacobiho rovnice
    - Základy teorie svazků, variační posloupnost
Literature
    recommended literature
  • D. Krupka. Jets and Contact Elements. Proc. of the Seminar on Differential Geometry, M, 2000. info
  • D. Krupka. The Geometry of Lagrange Structures II. - Elementary Sheaf Theory. Silesian University, Opava, 1998. info
  • D. Krupka. The Geometry of Lagrange Structures. Silesian University, Opava, 1997. info
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963. URL 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 Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2009, recent)
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