English

doc. Ing. Jiří Šremr, Ph.D.

Institute of Mathematics

Linear algebra, differential calculus of functions of one and several variables, integral calculus of functions of one variable, solving of linear ordinary differential equations and their systems, fundamentals of dynamical systems theory (in particular, autonomous systems of ODEs).

Attendance at lectures and seminars is obligatory and checked. Absence may be compensated for based on an agreement with the teacher. 

Course-unit credit is awarded on the following conditions: Active participation at seminars.

Examination: The exam tests the knowledge of definitions, theorems, and selected proofs and the ability to apply theoretical apparatus to the given problems. Detailed information will be announced at the end of the semester.

Aim of the course: The aim of the course is to acquaint the students with the advanced topics on the theory of stability of solutions to systems of non-autonomous differential equations and to show a possible use of the theoretical results in the analysis of stability of motions (not equilibria only) of mechanical systems with one or more degrees of freedom.

Acquired knowledge and skills: Students will acquire the skills to apply theoretical mathematical apparatus in analysing the stability of the equilibria and the periodic solutions to Hamiltonian systems in classical mechanics. They will thus be ready to study the chaotic behaviour of mechanical systems.

Programme N-MAI-A: Mathematical Engineering, Master's, elective

Programme N-MAI-P: Mathematical Engineering, Master's, elective

26 hours, compulsory

Proofs of the statement presented at lectures, examples.