MU:MU03024 Seminar in Real Analysis II - Course Information

MU03024 Seminar in Real Analysis II

Extent and Intensity

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

Guaranteed by

doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava

Prerequisites (in Czech)

MU03022 Seminar in Real Analysis I || MU03029 Seminar in Real Analysis I

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 II. The course serves for the practical exercises, the deepening of student knowledge and the solving problems from the journal The American Mathematical Monthly. Emphasis is placed on autonomous student work.

Syllabus

• 1. Integration
  - relations between Riemann and Lebesgue integral
  - relation between measurability, integrability and continuity
  - Henstock-Kurzweil integral
  2. Differentiation
  - Dini derivates
  - Continuity and differentiability
  - Differentiation of monotone functions
  - Points of discontinuity
  - The Banach-Mazurkiewicz theorem
  3. Functions of bounded variation and absolutely continuous functions

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)

The course can also be completed outside the examination period.

Teacher's information

Active participation in tutorials and handover of solved homework.

• Enrolment Statistics (Summer 2019, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2019/MU03024