MU10138 Selected Topics in Mathematical Analysis II

Mathematical Institute in Opava
Summer 2022
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petra Nábělková, Ph.D. (lecturer)
Guaranteed by
RNDr. Petra Nábělková, Ph.D.
Mathematical Institute in Opava
Timetable
Tue 8:05–9:40 R2
Prerequisites (in Czech)
( MU20011 Selected Topics in MA I || MU10134 Selected Topics in MA I || MU10137 Selected Topics in MA I ) && NOW ( MU10935 Selected Topics in MA II - Exe ) && 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 (in Czech)
Cílem předmětu je seznámit studenty ze základy těchto oblastí matematické analýzy: integrální počet funkcí více proměnných, křivkové a plošné integrály, diferenciální rovnice, komplexní analýza.
Syllabus
  • Double integral over rectangle
    Double integral over general closed domain
    Triple integral over right rectangular prism
    Triple integral over general closed domain
    Contour integral
    Properties of contour integrals, Green theorem
    Surface integral
    Stokes theorem, Gauss-Ostrogradski theorem
    Basic notions on differential equations
    Linear differential equations
    Systems of differential equations
    Basic notions on functions of one complex variable
    Complex infinite series
    Derivatives of complex functions
    Taylor and Laurent series
    Residues and their applications
Literature
    recommended literature
  • J. Škrášek, Z. Tichý. Základy aplikované matematiky II. SNTL, Praha, 1986. info
  • J. Stewart. Calculus. California, 1983. info
  • J. F. Hurley. Calculus. Philadelphia, 1980. info
  • S. I. Grossman. Calculus. Academic Press, 1977. info
    not specified
  • P. Burda, J. Doležalová. Matematika III. VŠB TU-Ostrava. ISBN 80-248-1195-2. info
  • M. Greguš, M. Švec, V. Šeda. Obyčajné diferenciálne rovnice. Alfa-SNTL, Bratislava-Praha, 1985. info
  • M. M. Guterman, Z. H. Nitecki. Differential equations : a first course. Philadelphia, 1984. info
  • F. Olejník, V. Šoltés. Zbierka úloh z vyššej matematiky II. VŠT Košice, 1983. info
  • M. A. Jevrgrafov. Funkce komplexní proměnné. Praha, 1981. 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)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021.
  • Enrolment Statistics (recent)
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