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Set-valued analysis

ДВВ.01.01

Обов’язкова дисципліна для ОП

Second

2023/2024

3 Semester

3

PLO4. Be able to determine the type of data integration required for a task.

Full-time form

To study the discipline successfully the student must meet the following requirements: 1. Successful mastering of the following disciplines: 1) Mathematical analysis. 2) Functional analysis. 3) Differential equations. 4) Control theory. 5) Mathematical modeling. 2. Knowledge: 1) Theoretical foundations and methods of research systems using functional analysis and control theory approaches. 2) Principles of constructing control systems. 3. Skills: 1) Solve the basic problems of the theory of differential equations. 2) Solve the basic problems of control theory. 3) Research the qualitative characteristics of mathematical models. 4) Formulate optimization problems for mathematical models. 5) Apply methods of mathematical and computer modeling to study systems and construct mathematical models. 4. Possession of: 1) Programming skills. 2) Skills in construction, analysis, and application of mathematical models to solve problems of multivalued analysis.

The purpose of the discipline consists of teaching students modern methods of multivalued analysis and theory of systems with the multivalued right part, applied problems that lead to the tasks of multivalued analysis, and increasing the level of fundamental mathematical training.

1. Bashniakov O.M., Harashchenko F.H., Pichkur V.V. Praktychna stiikist, otsinky ta optymizatsiia. –K.: Kyivskyi universytet. - 2008. –383 s. 2. Blagodatskih V.I. Vvedenie v optimal'noe upravlenie. – M.: Vysshaya shkola, 2001. – 239 s. 3. Pichkur V.V. Doslidzhennia zadach praktychnoi stiikosti dyferentsialnykh vkliuchen. – K.: Kyivskyi universytet, 2005. – 141 s. 4. Blagodatskih V.I. Teoriya differencial'nyh vklyuchenij. Chast' І. – M.: Izdatel'stvo Moskovskogo universiteta, 1979. – 89 s. 5. Aubin J.-P., Frankowska H. Set-Valued Analysis. -Boston: Birkhauser, 2009. — 473 p. 6. Aubin J.-P., Cellina A. Differential Inclusions. Set-Valued Maps and Viability Theory. -Berlin: Springer-Verlag, 1984. - 342 p.

Lectures, laboratory classes, self-study, the study of the recommended sources.

Semester assessment: The perfect score that can be obtained by a student is 60 points: 1. Test work №1: 20/12 points. 2. Laboratory work № 1: 15/9 points. 3. Laboratory work № 2: 15/9 points. 4. Laboratory work № 3: 15/9 points. Final assessment (in the form of an exam): - Perfect score that can be obtained by a student: 40 points. - Form of conducting: written work. - Types of tasks: 4 written tasks (2 theoretical questions and 2 practical tasks). - A student receives a positive grade in the discipline if his grade for the exam is not less than 24 (twenty-four) points. - A student is admitted to the exam if during the semester he: 1) scored a total of at least 36 points; 2) wrote a test for 9 or more points; 3) performed and timely submitted two laboratory works from the list of proposed works.

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