The department provides exposition of basic courses “mathematical analysis”, “differential equations” for students of such faculties as mechanics and mathematics, phylological, computer sciences.
Special cources for bachelors: "Subharmonic functions",
"Stability theory and Delay differential equations",
"The Laplace transform", "Harmonic Analysis", "Special chapters of operator theory".
Special cources for magisters: "Mathematical problems of the kinetic theory",
"Stabilizability problem for systems of controled differential equations",
"Harmonic analysis", "Distubution of values of meromorphic functions".
During 2005-2011 years on the department 15 text-books and methodical instructions for the high school were worked out, and a lot of individual tests and control tasks were prepared.
Special cources for bachelors:
- "Subharmonic functions"
- Introduction results: some questions of the theory of semicontinuous functions, some questions of the theory of harmonic functions.
It is considered such questions. Principles of maximum for subharmonic functions. Operations on subharmonic functions. Perron's method of solution
of Dirichlet problem. Representation Riesz theorem. Theory of capacity, fine topoligy.
- "Stability theory and Delay differential equations"
- Existence, uniqueness and properties of solutions to delay differential equations are studied.
We consider different types of delay: the simplest case - constant discrete delay, constant distributed delay, state-dependent delay.
The main interest is in qualitative properties of solutions.
- "The Laplace transform"
- The course starts with some basic definitions and examples in the Laplace transform theory. Later we discuss inversion formulas and some applications of the Laplace transform. (S.L.Gefter).
- "Harmonic Analysis"
- The course includes the following material: compact topological groups, the Haar Measure, unitary representations of compact topological groups, the Peter-Weil theorem, unitary representations of commutative compact groups, characters of commutative compact groups, Fourier series on commutative compact groups, Pontryagin Duality Theorem, some corollaries and examples. (S.L.Gefter).
Special cources for magisters:
- "Mathematical problems of the kinetic theory"
- The main equation of the kinetic theory of a Gas, namely nonlinear integro-differential Boltzmann equation, is considered
for various models of interaction between the molecules. The exact and the approximate solutions of this equation are studied.
More details are on the Ukrainian web-page.
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