MU25006 Global Analysis

Mathematical Institute in Opava
Winter 2012
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Michal Marvan, 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
Syllabus (in Czech)
  • Algebra hladkých funkci na varietách a její diferencování
    - Rank, imerze a submerze
    - Orientovatelnost, objemový element, integrování na orientovatelných varietách
    - Stokesova věta a její speciální p!ípady
    - Integrování na varietě s metrickým polem, Hodgeova dualita
    - Poincarého lemma, de Rhamovy kohomologie, Poincaréova dualita
    - Kritické body a Sardova věta; Whitneyho věty
    - Poincarého lemma, de Rhamovy kohomologie, Poincaréova dualita
    - Kritické body a Sardova věta; Whitneyho věty
Literature
    recommended literature
  • L. Krump, V. Souček, J. A. Tůšínský. Matematická analýza na varietách. Praha, Karolinum, 1998. info
  • D. Krupka. Úvod do analýzy na varietách. SPN, Praha, 1986. info
  • O. Kowalski. Základy matematiké analýzy na varietách. Univerzita Karlova, Praha, 1975. info
  • F. Warner. Foundations of differentiable manifolds and Lie groups. Springer-Verlag, N.Y.-Berlin, 1971. info
  • R. Narasimhan. Analysis on real and complex manifolds. North-Holland Publishing Company, Amsterdam, 1968. info
  • M. Spivak. Calculus on Manifolds. 1965. info
Language of instruction
English
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020.
  • Enrolment Statistics (Winter 2012, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2012/MU25006