MU03023 Real Analysis II

Mathematical Institute in Opava
Summer 2017
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Marta Štefánková, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU03021 Real Analysis I || MU03028 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 (in Czech)
Náplní přednášky jsou pokročilejší partie z teorie integrálu, diferencovatelnost funkcí a vztah derivací a integrálu.
Syllabus
  • Relationship between Lebesgue and Riemann integrals
    Measurability, integrability and continuity
    Generalizations, Henstock-Kurzweil integral
    Continuity and differentiability
    Differentiability of monotonous functions
    Points of discontinuity of a function
    Banach-Mazurkiewicz theorem
    Derivative of a function discontinuous on a dense set
    Functions of bounded variation
    Absolutely continuous functions
    Differentiability in normed spaces
    Approximation of real functions
    Stone-Weierstrass theorem
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.
The course is also listed under the following terms Summer 2015, Summer 2016, Summer 2018, Summer 2019, Summer 2020, Summer 2022.
  • Enrolment Statistics (Summer 2017, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2017/MU03023