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MU:MU20003 Mathematical Analysis III - Course Information

## MU20003 Mathematical Analysis III

**Mathematical Institute in Opava**

Winter 2021

**Extent and Intensity**- 4/2/0. 7 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- doc. RNDr. Michal Málek, Ph.D. (lecturer)

Mgr. Jan Tesarčík, Ph.D. (seminar tutor) **Guaranteed by**- doc. RNDr. Michal Málek, Ph.D.

Mathematical Institute in Opava **Timetable**- Tue 9:45–11:20 RZ, Thu 8:55–10:30 R1
- Timetable of Seminar Groups:

*J. Tesarčík* **Prerequisites**(in Czech)-
**MU20002**Mathematical Analysis II &&**MU20006**Algebra II && 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**- Aim of this third part of basic course of mathematical analysis is to present basic principles of differential calculus of several variables.
**Syllabus**- 1. Functions of several variables

Normed speces, topology of a normed space, equivalent norms, equivalence of all the norms in finite-dimensional spaces, the natural topology, basic normes, compact sets, limit and continuity of mappings.

2. The first derivative

Fréche derivative, Gateaux derivative, directional derivative, partial derivative, differential, their basic properties and relations between them, Chain Rule, continuous differentiability.

3. Theorems on inverse function and on imlicite function

Theorem on imlicite function and its derivative,Theorem on inverse function adn its derivative.

4. Higher derivatives

Definition and properties of higher derivatives, symmetry of higher derivatives, higher partial derivatives, Taylor formula.

Extreme problems with and without constrains, Lagrange Theorem on multiplicators.

- 1. Functions of several variables
**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 (recent)

- Permalink: https://is.slu.cz/course/sumu/winter2021/MU20003