#
MU:MU20004 Mathematical Analysis IV - Course Information

## MU20004 Mathematical Analysis IV

**Mathematical Institute in Opava**

Summer 2022

**Extent and Intensity**- 3/2/0. 7 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- 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 **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**- Mathematical Methods and Modelling (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)

**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.
**Syllabus**- 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.

- 1. Riemann integral
**Literature****Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- The examination consists of a written and of an oral part.

- Enrolment Statistics (Summer 2022, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2022/MU20004