Infopaket

Modern problems of analysis

Вибіркова дисципліна для ОП

First

2023/2024

6 Semester

5

LO 8. Combine methods of mathematical and computer modeling with informal expert analysis procedures to find optimal solutions. LO 19. Collect and interpret relevant data and analyze complexities within their specialization to make judgments that reflect relevant social and ethical issues. PLO 21.1. Understand the main areas of applied mathematics and computer science, to the extent necessary for the development of general professional mathematical disciplines, applied disciplines and the use of their methods in the chosen profession.

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.

This discipline is designed to provide students with knowledge of modern sections of nonlinear analysis such as the theory of nonstretching operators, the theory of monotone operators, methods for studying variational inequalities, regularization methods, methods for approximating fixed points and methods for solving variational inequalities. The student who has successfully studied the course will be guided in the modern scientific literature on the range of issues.

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. Berezansky Yu.M., G.F.Us, Sheftel Z.G. Functional analysis. Kiev: Vishcha schola, 1990. Gaevsky H., Gröger K., Zacharias K. Nonlinear operator equations and operator differential equations. Moscow: Mir, 1978. Yosida K. Functional analysis. Moscow: Mir, 1967. Sea J. Optimization. Theory and algorithms. Moscow: Mir, 1973. Tikhonov A.N., Arsenin V.Ya. Methods for solving ill-posed problems. Moscow: Nauka, 1979. 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, LO 1.3, LO 2.1, LO 3.1 - 30 points / 18 points. 2. Test work 2: LO 1.1., LO 1.2, LO 1.3, LO 2.1, LO 3.1 - 30 points / 18 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 1.3, LO 2.1; - form and types of tasks: writing. Types of tasks: 4 writing tasks.

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