MU03037 Global Analysis II

Mathematical Institute in Opava
Summer 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
Prerequisites (in Czech)
MU03036 Global Analysis I
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
Methods of Analysis are extended from open subsets of R^n to spaces of more complicated topology -- smooth manifolds. The first part of this two-semester course covers, among others, integral calculus on varieties in a coordinate-independent presentation.
Syllabus
  • Smooth forms and tensors, tensor product, antisymmetric (exterior) forms, exterior differential, orientability, integration on orientable manifolds, Stokes theorem.
    Poincaré lemma, de Rham cohomology, degree of a mapping S^n -> S^n.
    Lie derivative.
    Lie groups and algebras, left-invariant vectorová fields, exponential mapping, examples.
    Rank, immersion and submersion, Sard theorem, Whitney theorems.
Literature
    recommended literature
  • L. Krump, V. Souček, J. A. Těšínský. 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
  • R. Narasimhan. Analysis on real and complex manifolds. North-Holland Publishing Company, Amsterdam, 1968. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Written and oral examination.
The course is also listed under the following terms Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012.
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