MU:MU03022 Seminar in Real Analysis I - Course Information

MU03022 Seminar in Real Analysis I

Extent and Intensity

0/2/0. 2 credit(s). Type of Completion: z (credit).

Teacher(s)

RNDr. Lenka Rucká, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava

Timetable of Seminar Groups

MU03022/01: Tue 8:05–9:40 R2, L. Rucká

Prerequisites (in Czech)

TYP_STUDIA(BN)

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 Analysis (programme MU, N1101)
• Mathematics (programme MU, B1101)

Course objectives

The scope and content of the seminar is above all curriculum of the course of Real Analysis I. The course serves for the practical exercises and the deepening of student knowledge. Emphasis is placed on autonomous student work.

Syllabus

• 1. Measures
  - Definitions and basic properties
  - Outer measure
  - Carathéodory's theorem
  - Hausdorff measure
  - Lebesgue-Stieltjes measure
  2. Measurable functions
  - Definitions and basic properties
  - Approximation of measurable function by simple measurable functions
  - Sequences of measurable functions
  3. Integration
  - Definitions and basic properties
  - Limit properties of integrals
  - Lebesgue and Lebesgue-Stieljes integral

Literature

recommended literature
• A. M. Bruckner, J. B. Bruckner, B. S. Thomson. Real Analysis. Upper Saddle River, New Jersey, 1997. ISBN 0-13-458886-X. info
• M. Švec, T. Šalát, T. Neubrunn. Matematická analýza funkcií reálnej premennej. Bratislava, 1987. 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

Active participation in tutorials and handover of solved homework.

• Enrolment Statistics (recent)
  
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