MU:MU03265 Variational Analysis on Manif. - Course Information

MU03265 Variational Analysis on Manifolds

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

• 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)
• Upper Secondary School Teacher Training in Mathematics (programme MU, N1101)
• Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)

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.

• Enrolment Statistics (Summer 2010, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2010/MU03265