Course unit code:
Course unit title:
Selected Topics in Mathematics
Mode of completion and Number of ECTS credits:
Exm (2 credits)
Course supervisor:
doc. RNDr. Soňa Pavlíková, CSc.
Name of lecturer(s):
T. Visnyai (2022/2023 – Winter)
T. Visnyai (2021/2022 – Winter)
S. Pavlíková (2020/2021 – Winter)
S. Pavlíková (2019/2020 – Winter)
S. Pavlíková (2017/2018 – Winter)
S. Pavlíková (2016/2017 – Winter)
S. Pavlíková (2015/2016 – Winter)
Learning outcomes of the course unit:
Acquire the theoretical foundations of the differential equations, functional analysis and calculus of variations.
Prerequisites for registration:
Course contents:
Basic terms and some properties of linear differential equations. Homogenous and non-homogenous linear differential equations. Systems of linear differential equations. Transformations of continuous systems to discrete systems. Norm, norm spaces and sub-spaces, complete spaces, basic examples and properties. Norms in Euclid space and space of functions.. Functional in linear norm spaces, functional examples and properties. Examples of more complicated functional. Case of more variables. Higher functional derivations. Necessary and sufficient conditions for fixed extreme. Lagrange function method. Isoperimetric problem. Lagrange task. Non-linear programming problem and Kuhn-Tucker conditions of optimality. Optimal control problem. Basic terms. Problem with fixed ending points. Problem with free ending points in plane and 3-dimensional space.
Recommended or required reading:
  • HAMALA, M. – TRNOVSKÁ, M. Nelineárne programovanie. Bratislava: EPOS, 2013. 339 s. ISBN 978-80-8057-986-9.
  • BRUNOVSKÝ, P. – HALICKÁ, M. – JURČA, P. Optimálne riadenie. Bratislava: EPOS, 2009. ISBN 978-80-8057-793-3.
  • TICHÝ, Z. – ŠKRÁŠEK, J. Základy aplikované matematiky I. Praha: SNTL, 1989. 876 s.
  • TICHÝ, Z. – ŠKRÁŠEK, J. Základy aplikovanej matematiky II. Praha: SNTL, 1986. 896 s.
  • TICHÝ, Z. – ŠKRÁŠEK, J. Základy aplikovanej matematiky III. Praha: SNTL, 1990. 853 s.
  • POZNYAK, A S. Advanced Mathematical Tools for Automatic Control Engineers. Amsterdam: Deterministic Techniques, 2008. 774 s. ISBN 978-0-08-044674-5.
  • F, S. – G, I. Calculus of variations. New York: Dover publications,inc.: Mineola, 2000. 232 s. ISBN 978-0-486-41448-5.
Planned learning activities and teaching methods:
The object is realized in the form of lectures and exercises.
Assesment methods and criteria:
credit, examination
Language of instruction:
Slovak, English
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