## 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:
MU20003/01: Wed 11:25–13:00 R2, 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
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.
Literature
required literature
• L. Zajíček. Vybrané partie z matematické analýzy pro 2. ročník. Praha, 2007. ISBN 978-80-7378-027-2. info
• R. Sikorski. Advanced Calculus. Functions of Several Variables. Polish Scientific Publishers, 1969. ISBN 978-0028522807. info
recommended literature
• V. I. Averbuch, M. Málek. Matematická analýza III, IV. Opava, 2003. URL info
• K. Rektorys a spolupracovníci. Přehled užité matematiky. SNTL, Praha, 1968. info
• V. Jarník. Diferenciální počet I. ČSAV, Praha, 1963. info
• V. Jarník. Diferenciální 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.
Teacher's information
The examination consists of a written and of an oral part.
The course is also listed under the following terms Winter 2020.
• Enrolment Statistics (recent)