MU:MU25006 Global Analysis - Course Information

MU25006 Global Analysis

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava

Timetable of Seminar Groups

MU25006/01: No timetable has been entered into IS. P. Vojčák

Prerequisites (in Czech)

TYP_STUDIA(BN)

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, 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.
  

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 (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.

Activity	Difficulty [h]
Cvičení	26
Přednáška	26
Summary	52

• Enrolment Statistics (Winter 2019, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2019/MU25006