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Course, academic year 2023/2024
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Theory of Real Functions 2 - NMMA404
Title: Reálné funkce 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Class: M Mgr. MA
M Mgr. MA > Povinné
Classification: Mathematics > Real and Complex Analysis
Incompatibility : NRFA013
Interchangeability : NRFA013
Is interchangeable with: NRFA013
Annotation -
Last update: doc. RNDr. Pavel Pyrih, CSc. (13.05.2022)
The course is devoted to several basic results of geometric measure theory and to deeper results on derivatives and B1 functions.
Course completion requirements -
Last update: doc. RNDr. Miroslav Zelený, Ph.D. (17.02.2023)

The exam is oral. The required knowledge corresponds to the sylabus at the presented extent.

Literature -
Last update: T_KMA (25.04.2013)

Kechris, Alexander S.: Classical descriptive set theory. Graduate Texts in Mathematics, 156. Springer-Verlag, New York, 1995.

Oxtoby, John C. Measure and category. A survey of the analogies between topological and measure spaces. Second edition. Graduate Texts in Mathematics, 2. Springer-Verlag, New York-Berlin, 1980

Requirements to the exam -
Last update: doc. RNDr. Petr Holický, CSc. (25.02.2021)

The exam is oral or via zoom. The required knowledge corresponds to the sylabus at the presented extent.

Syllabus -
Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (09.05.2022)

1. area a coarea formulae

2. semicontinuous functions, functions of the first Baire class

3. density topology, approximate continuity and differentiability

4. a deeper view on derivatives

5. sets with a finite perimeter, divergence theorem

Entry requirements -
Last update: doc. RNDr. Petr Holický, CSc. (25.02.2021)

Theory of metric spaces, as covered by lectures NMMA201 and NMMA202.

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