Functional analysis

Course: Applied Mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Functional analysis
Code
Module type
Обов’язкова дисципліна для ОП
Educational cycle
First
Year of study when the component is delivered
2022/2023
Semester/trimester when the component is delivered
4 Semester
Number of ECTS credits allocated
4
Learning outcomes
LO 18. Efficiently communicate with the supply of information, ideas, problems and solutions with specialists and support
Form of study
Prerequisites and co-requisites
To successfully learn the discipline “Functional analysis” the student should satisfy the following requirements. They have successfully passed the courses “Calculus”. They know (a) fundamentals of Calculus. They can (a) solve problems of Calculus. They should be able to (a) seek information in the Internet.
Course content
Block 1. Spaces Topological structures Методи введення топології Неперервні відображення і гомеоморфізми Компактність Метричні простори Повні метричні простори Лінійні простори Нормовані простори Test work Block 2. Operator theory Space of linear bounded operators Uniform boundedness principle Open mapping principle Euclidean spaces Hilbert space Isomorphism theorem Test work 2 h.
Recommended or required reading and other learning resources/tools
1. Aleksandrian R.A., Mirzakhanian E.A. Obshchaia topologiia. - M.:Vysshaia shkola, 1979. - 336 s. 2. Arkhangel-skii A. V., Ponomarev V. I. Osnovy obshchei topologii v zadachakh i uprazhneniiakh. – M., 1974; 3. Berezanskii Iu.M., G.F.Us, Sheftel- Z.G. Funktsional-nyi analiz. - K.: Vishcha shkola, 1990. - 600 s. 4. Vulikh B.Z. Vvedenie v funktsional-nyi analiz. - M.: Nauka, 1967. - 416 s. 5. Kantorovich L.V., Akilov G.P. Funktsional-nyi analiz. - M.: Nauka, 1984. - 752 s. 6. Kliushin D.A., Semenov V.V. Zadachі ta vpravi z kursu “Funktsіonal-nii analіz”. Elementi zagal-noї topologії. – K.: Vidavnicho-polіgrafіchnii tsentr "Kiїvs-kii unіversitet", 2005. – 67 s. 7. Kliushin D.A., Semenov V.V. Zadachі ta vpravi z kursu “Funktsіonal-nii analіz”. Lіnіinі normovanі prostori ta lіnіinі neperervnі funktsіonali. – K.: Vidavnicho-polіgrafіchnii tsentr "Kiїvs-kii unіversitet", 2006. – 39 s.
Planned learning activities and teaching methods
Lectures, seminars, 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

Departments

The following departments are involved in teaching the above discipline