Course: Real Analysis II

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Course title Real Analysis II
Course code MU/03030
Organizational form of instruction Lecture
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • ŠTEFÁNKOVÁ Marta, doc. RNDr. Ph.D.
Course content
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

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


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Summer