MU25006 Global Analysis

Mathematical Institute in Opava
Winter 2013
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
RNDr. Adam Hlaváč, Ph.D. (seminar tutor)
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
  • 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.
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
Czech
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2012, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020.
  • Enrolment Statistics (Winter 2013, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2013/MU25006