MU20012 Selected Topics in Mathematical Analysis II

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
2/2/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Karel Hasík, Ph.D. (lecturer)
Mgr. Jan Tesarčík, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava
Timetable
Tue 10:35–12:10 20
  • Timetable of Seminar Groups:
MU20012/01: Thu 9:45–11:20 203, J. Tesarčík
Prerequisites (in Czech)
MU20011 Selected Topics in MA I && 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 objective of this course is to provide an introduction to the integral calculus of several variables and complex analysis. The curriculum aims at applications.
Syllabus
  • 1. Riemann integral
    - integrals over elementary region and over general closed region, Fubini's theorem, substitutions
    2. Integration of differential forms
    - contour integrals of the first and second kind
    - Green theorem
    - applications of contour integrals
    - surface integrals of the first and second kind
    - Stokes theorem, Gauss-Ostrogradski theorem
    - applications of surface integrals
    3. Basics of complex analysis
    - functions of one complex variable
    - derivatives and integrals in the complex domain
    - Taylor and Laurent series
    - Cauchy's residue theorem and its consequences
Literature
    required literature
  • S. Lang. Calculus of Several Variables. Springer, 1996. info
  • J. Škrášek, Z. Tichý. Základy aplikované matematiky II. SNTL, Praha, 1986. info
  • M. A. Jevgrafov. Funkce komplexní proměnné. Praha, 1981. info
    recommended literature
  • I. Černý. Foundations of Analysis in the Complex Domain. Ellis Horwood Ltd, 1993. info
  • J. Stewart. Calculus. California, 1983. info
  • J. F. Hurley. Calculus. Philadelphia, 1980. info
  • S. I. Grossman. Calculus. Academic Press, 1977. info
  • I. Černý. Základy analýzy v komplexním oboru. Academia, Praha, 1967. info
    not specified
  • P. Burda, J. Doležalová. Matematika III. VŠB TU-Ostrava. ISBN 80-248-1195-2. info
  • V. Jarník. Integrální počet I. ČSAV, Praha, 1963. info
  • V. Jarník. Integrální počet II. ČSAV, Praha, 1963. 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
Requirements for pre-exam credits are active participation in tutorials and reaching at least 60% overall in partial tests. The examination comprises two part - written and oral.
The oral part follows the successful written part and verifies professional knowledge and skills resulting from the course.

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