MU03031 Seminar in Real Analysis II

Mathematical Institute in Opava
Summer 2013
Extent and Intensity
0/2/0. 4 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Lenka Rucká, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jaroslav Smítal, DrSc.
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
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.
The course is also listed under the following terms Summer 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020.
  • Enrolment Statistics (Summer 2013, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2013/MU03031