Complementary chapters of functional analysis/ Module 1. Applied functional analysis.

Course: Applied mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Complementary chapters of functional analysis/ Module 1. Applied functional analysis.
Code
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2021/2022
Semester/trimester when the component is delivered
1 Semester
Number of ECTS credits allocated
6
Learning outcomes
PLO3. Gaining knowledge for the ability to evaluate existing technologies and on the basis of analysis to form requirements for the development of advanced information technologies.
Form of study
Prerequisites and co-requisites
To successfully learn the discipline “Complementary chapters of functional analysis. Module 1. Applied Functional Analysis” the student should satisfy the following requirements. They have successfully passed the courses Calculus, Functional analysis, and Linear Algebra. They know (a) fundamentals of Calculus, Functional analysis, and Linear Algebra . They can (a) solve problems of Calculus, Functional analysis, and Linear Algebra. They should be able to (a) seek information in the Internet.
Course content
Block 1. Filters and nets. Nets Filters and bases of filters. Limits and limit points of filters. Ultrafilters. Criteria of compactness. Connection between filters and nets Nopology induced by a family if sets Tikhonov topology Test work Block 2. Topological vector spaces. Fundamentals of topological vector spaces Completeness and compactness in topological vector spaces Linear operators and functionals Locally convex spaces Weak topologies General notions of duality Duality in locally convex spaces Duality in Banach spaces Krein–Milman theorem Test work
Recommended or required reading and other learning resources/tools
1. Kadets V.M. Kurs funktsionalnogo analiza. — H.: HNU im. V.N. Karazina, 2006. — 608 s. 2. Aleksandryan R.A., Mirzahanyan E.A. Obschaya topologiya. - M.:Vyisshaya shkola, 1979. - 336 s. 3. Berezanskiy Yu.M., G.F.Us, Sheftel Z.G. Funktsionalnyiy analiz. - K.: Vischa shkola, 1990. - 600 s. 4. Kantorovich L.V., Akilov G.P. Funktsionalnyiy analiz. - M.: Nauka, 1984. - 752 s. 5. Kolmogorov A.N. Fomin S.V. Elementyi teorii funktsiy i funktsionalnogo analiza.- M: Nauka, 1981. - 544 s. 6. Kelli Dzh. Obschaya topologiya. – M.: Nauka, 1981. 7. Engelking R. Obschaya topologiya. – M.: Mir, 1986.
Planned learning activities and teaching methods
Lectures, independent work, recommended literature processing, homework.
Assessment methods and criteria
Intermediate assessment: The maximal number of available points is 60. Test work no. 1: RN 1.1, RN 1.2 – 30/18 points. Test work no. 2: RN 1.1, RN 1.2 – 30/18 points. Final assessment (in the form of exam): The maximal number of available points is 40. The results of study to be assessed are RN 1.1, RN 1.2, RN 2.1, and RN 3.1. The form of exam: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Dmytro Anatoliiovych Klyushin
Computational Mathematics
Faculty of Computer Science and Cybernetics

Departments

The following departments are involved in teaching the above discipline

Computational Mathematics
Faculty of Computer Science and Cybernetics