MU:MU20012 Selected Topics in MA II - Course Information
MU20012 Selected Topics in Mathematical Analysis IIMathematical Institute in Opava
- Extent and Intensity
- 2/2/0. 7 credit(s). Type of Completion: zk (examination).
- 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
- Tue 10:35–12:10 20
- Timetable of Seminar Groups:
- 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.
- 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
- 1. Riemann integral
- 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
- 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
- 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.
- Enrolment Statistics (recent)
- Permalink: https://is.slu.cz/course/sumu/summer2021/MU20012