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Advanced functional analysis. Module 1. Applied functional analysis. Module 2. Convex and nonlinear

Вибіркова дисципліна для ОП

Second

2021/2022

1 Semester

6

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.

Know the basic concepts and facts of mathematical analysis, functional analysis 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.

Obtaining basic knowledge of applied functional analysis, mastering the techniques of solving applied problems using the methods of functional analysis. Obtaining knowledge of modern convex and nonlinear functional analysis. As a result of studying the discipline the student must: know the theory of duality, basic facts about convex sets and functions, methods of approximation of fixed points; be able to apply the studied methods and results in the study of typical issues related to the analysis of mathematical models: the existence, correctness, construction of an approximate method.

Kadets V.M. Functional Analysis Course. Kh.: KhNU im. V.N. Karazina, 2006. Aleksandryan R.A., Mirzakhanyan E.A. General topology. Moscow: Vischaya schkola, 1979. Kantorovich L.V., Akilov G.P. Functional analysis. Moscow: Nauka, 1984. 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. Aubin J.-P., Ekland I. Applied nonlinear analysis. Moscow: Mir, 1988. Kinderlehrer D., Stampacchia G. Introduction to variational inequalities and their applications. Moscow: Mir, 1983. Ekland I., Temam R. Convex analysis and variational problems. Moscow: Mir, 1979.

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

Maximum number of points that can be obtained by a student: 100/60 points. - Intermediate assessment: 1. Test work 1: LO 1.1., LO 1.2 - 10 points / 6 points. 2. Test work 2: LO 1.1., LO 1.2 - 10 points / 6 points. 3. Independent work 1: LO 1.1, LO 2.1, LO 3.1 - 20 points / 12 points. 4. Independent work 2: LO 1.1, LO 2.1, LO 3.1 - 20 points / 12 points. - Final assessment (in the form of exam): - the maximum number of points that can be obtained by a student: 40 points; - learning outcomes that will be evaluated: LO 1.1, LO 1.2, LO 2.1; - form and types of tasks: writing. Types of tasks: 4 writing tasks.

Ukrainian