MU25006 Global Analysis

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
RNDr. Hynek Baran, Ph.D. (lecturer)
Mgr. Jakub Vašíček (seminar tutor)
Guaranteed by
RNDr. Hynek Baran, Ph.D.
Mathematical Institute in Opava
Tue 9:45–11:20 205
  • Timetable of Seminar Groups:
MU25006/01: Wed 16:25–18:00 203, J. Vašíček
Prerequisites (in Czech)
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
  • Algebra of smooth functions on a manifold and its derivations.
    Rank, immersion and submersion.
    Orientability, volume element, integration on oriented manifolds.
    Stokes theorem and its special cases.
    Integration on a manifold with metric field, Hodge duality.
    Poincare lemma, de Rham cohomology, Poincare duality.
    Critical points and Sard theorem; Whitney theorems.
    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
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
To obtain the course credits it is necessary to actively participate in the seminar and solve homework problems. The additional potential requirements are set by the tutor. The final exam consists of a written and an oral part. In the written part, it is necessary to solve two assigned problems and potentially be able to explain some details of the solutions. The oral part comprises two theoretical questions.
ActivityDifficulty [h]
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
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