14. 12. 2019  8:45 Branislava, Bronislava
Akademický informačný systém

Sylabus predmetu DYSY06_6I - Dynamic Systems (MTF - SS 2020/2021)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Materials Science and Technology in Trnava
Course unit code: DYSY06_6I
Course unit title: Dynamic Systems
Mode of delivery, planned learning activities and teaching methods:
lecture1 hour weekly (on-site method)
13 hours per semester of study (combined method)
seminar1 hour weekly (on-site method)
13 hours per semester of study (combined method)

 
Credits allocated: 3
 
Recommended semester/trimester: -- item not defined --
Level of study: 2.
Prerequisites for registration: none
 
Assesment methods:
-- item not defined --
 
Learning outcomes of the course unit:
The main purpose of the module is to acquaint students with both theoretical and practical aspects of mathematical models and analytical methods in the mathematical theory of dynamical systems ant their numerical simulation.
 
Course contents:
1. Linear dynamical systems x’=Ax. Eigenvalues and eigenvectors of the matrix A. Jordan canonical form of planar systems. The direct methods for solving linear dynamical systems.
2. Nonlinear dynamical systems. The local dynamics near hyperbolic equilibrium points. Hartman–Grobman theorem
3. Important structural properties of dynamical systems – stability (Lyapunov’s methods), controllability, observability (Kalman’s theory).
 
Recommended or required reading:
Basic:
PERKO, L. Differential Equations and Dynamical Systems. New York : Springer Verlag, 2001. 555 p. ISBN 0-387-95116-4.
RALSTON, A. -- VITÁSEK, E. -- PRÁGER, M. Základy numerické matematiky. Praha : Academia, 1978. 635 p.
VRBAN, A. -- MORAVČÍK, O. Citlivosť, tolerantnosť a robustnosť dynamických systémov. Bratislava : STU v Bratislave, 2006. 81 p. ISBN 80-227-2422-X.
KROKAVEC, D. -- FILASOVÁ, A. Diagnostika dynamických systémov. Košice : Elfa, 2007. 238 p. ISBN 978-80-8086-060-8.
JIRÁSEK, F. -- VACEK, M. -- POLÁŠEK, J. Funkce komplexní proměnné a Laplaceova transformace. Praha : České vysoké učení technické v Praze, 1983. 229 p.
ROVDER, J. Vybrané state z matematiky: Funkcie komplexnej premennej. Laplaceova transformácia. Parciálne diferenciálne rovnice 2.rádu. Bratislava : SVŠT v Bratislave, 1986. 209 p.

 
Language of instruction: slovak or english
 
Notes:
 
Courses evaluation:
Assessed students in total: 376

ABCDEFX
27,4 %17,0 %20,5 %13,6 %20,2 %1,3 %
Name of lecturer(s): doc. Mgr. Róbert Vrábeľ, PhD. (examiner, instructor, lecturer, person responsible for course, tutor) - slovak
 
Last modification: 15. 8. 2019
Supervisor: doc. Mgr. Róbert Vrábeľ, PhD. and programme supervisor


Last modification made by Ing. Erika Kuracinová on 08/15/2019.

Typ výstupu: