MU20003 Mathematical Analysis III

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
4/2/0. 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
Timetable
Mon 13:05–14:40 309, Tue 8:55–10:30 BF - BrainFitness
  • Timetable of Seminar Groups:
MU20003/01: Thu 8:05–9:40 R1, P. Vojčák
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)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
The examination consists of a written and of an oral part.

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