MU03030 Real Analysis II

Mathematical Institute in Opava
Summer 2018
Extent and Intensity
2/0/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Marta Štefánková, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU03021 Real Analysis I || MU03028 Real Analysis I || MU18023 Real Analysis I
Course Enrolment Limitations
The course is offered to students of any study field.
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
    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 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 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2019.
  • Enrolment Statistics (Summer 2018, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2018/MU03030