MU20004 Mathematical Analysis IV

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
3/2/0. 7 credit(s). Type of Completion: zk (examination).
RNDr. Petr Blaschke, Ph.D. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava
Tue 8:05–10:30 RZ
  • Timetable of Seminar Groups:
MU20004/01: Thu 9:45–11:20 R2, P. Vojčák
Prerequisites (in Czech)
MU20003 Mathematical Analysis III && TYP_STUDIA ( B )
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
The main attention of the fourth part of the basic course of mathematical analysis is given to Riemann integral, including Lebesgue Theorem and Fubini Theorem, change of variables and Stokes Theorem for manifolds. Last chapter is devoted to komplex analysis.
  • 1. Riemann integral
    Integral on elementary sets, Integral on general closed sets, Fubini Theorem, change of variables in integral.
    2. Differential forms
    Integration on manifolds, basic properties, applications: line and surface integral,
    Green, Stokes, Gauss-Ostrogradsky Theorem and general Stokes Theorem.
    3. Elements of comlex analysis
    Functions of one comlex variable, derivative and integral for such functions, Taylor and Laurent series, residues.
    required literature
  • V. I. Averbuch, M. Málek. Matematická analýza III, IV. Opava, 2003. URL info
  • V. Jarník. Integrální počet I. ČSAV, Praha, 1963. info
  • V. Jarník. Integrální počet II. ČSAV, Praha, 1963. info
    recommended literature
  • W. Rudin. Analýza v reálném a komplexním oboru. Academia, Praha, 1987. info
  • M. Spivak. Matematičeskij analiz na mnogoobrazijach. Mir, Moskva, 1968. info
  • W. Rudin. Real and Complex Analysis. 1966. 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
The examination consists of a written and of an oral part.

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