MU03023 Real Analysis II

Mathematical Institute in Opava
Summer 2020
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Lenka Rucká, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava
Timetable
Tue 8:05–9:40 117
Prerequisites (in Czech)
( MU03021 Real Analysis I || MU03028 Real Analysis I ) && 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
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)
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2022.
  • Enrolment Statistics (Summer 2020, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2020/MU03023