Infopaket

Methods of analysis of operator systems

Обов’язкова дисципліна для ОП

Second

2023/2024

3 Semester

3

PLO1. Be able to use of in-depth professional knowledge and practical skills to optimize the design of models of any complexity, to solve specific problems of designing intelligent information systems of different physical nature. PLO6. Be able to design and use existing data integration tools, process data stored in different systems.

Know the basic concepts and facts of mathematical analysis, functional analysis, equations of mathematical physics and linear algebra. Be able to solve typical problems in mathematical analysis, functional analysis, and linear algebra. Have basic skills of searching for information on the Internet.

Gaining knowledge of the principles of linear functional analysis, the theory of linear operator equations, the theory of generalized solutions of linear operator equations, methods of studying the existence of solutions of mathematical physics, elements of the theory of incorrect problems and their regularization. This knowledge will help to apply fundamental mathematical constructions to solve practical problems in various applied fields and to navigate in the modern scientific literature.

Berezansky Yu.M., G.F.Us, Sheftel Z.G. Functional analysis. K .: Vishcha schola, 1990. Bauschke H.H., Combettes P.L. Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, 2011. Goebel K., Kirk W.A. Topics in metric fixed point theory. Cambridge University Press, 1990. Crane S.G. Linear equations in a Banach space. Moscow: Nauka, 1971. Lyashko S.I., Nomirovskiy D.A., Petunin Yu.I., Semenov V.V. Hilbert's twentieth problem. Generalized solutions of operator equations. Moscow: OOO I.D. Williams, 2009. Tikhonov A.N., Arsenin V.Ya. Methods for solving ill-posed problems. Moscow: Nauka, 1979.

Lectures, independent work, recommended literature processing, homeworks, test works.

- Intermediate assessment: 1. Test work 1: LO 1.1, LO 1.2, LO 2.1 - 40 points / 24 points. 2. Test work 2: LO 1.1, LO 1.2, LO 2.1 - 40 points / 24 points. 3. Current assessment in lectures: LO 1.1, LO 1.2, LO 2.1, LO 3.1, LO 4.1, LO 4.2 - 20 points. - Final assessment: the test is based on the results of the student's work throughout the semester and does not provide additional assessment activities for successful students. - conditions of admission to the final test: it is necessary to successfully write tests.

Ukrainian