MU:MU25006 Global Analysis - Course Information
MU25006 Global Analysis
Mathematical Institute in OpavaWinter 2014
- 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
- Geometry and Global Analysis (programme MU, N1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematical Analysis (programme MU, N1101)
- Mathematics (programme MU, B1101)
- 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.
- Algebra of smooth functions on a manifold and its derivations.
- 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.
- Enrolment Statistics (Winter 2014, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2014/MU25006