Infopaket

Applied stability problems

ДВС.2.03

Вибіркова дисципліна для ОП

First

2022/2023

7 Semester

23

PLO1. Demonstrate knowledge and understanding of basic concepts, principles, and theories of fundamental and applied mathematics and use them in practice. PLO2. Know basic principles and methods of mathematical, complex, and functional analysis, linear algebra and number theory, analytical geometry, theory of differential equations, including equations of mathematical physics, probability theory, mathematical statistics, and random processes, numerical methods. PLO4. Perform mathematical description, analysis, and synthesis of discrete objects and systems, using the concepts and methods of discrete mathematics and algorithm theory. PLO5. PLO6. PLO9. PLO11. PLO14. PLO15. PLO16. PLO19. PLO20. PLO21. PLO22.2. PLO23.2. PLO24.2. PLO25.2. PLO26.2. http://csc.knu.ua/media/filer_public/6a/29/6a29dc9d-47c9-46ef-aacd-67e1d899140e/opp_pm_2018__1.pdf

Full-time form

1. Successful mastering of the following disciplines: 1) Mathematical analysis. 2) Functional analysis. 3) Linear algebra 4) Differential equations. 5) Control theory 2. Knowledge: 1. Theoretical foundations and methods of construction, verification, and the study of quantitative and qualitative properties of mathematical models. 2. Principles of analysis and optimization of control systems. 3. Numerical methods for finding solutions of differential equations and systems of differential equations. 3. Skills: 1. Solve the basic problems of differential equations theory. 2. Research the properties of functions. 3. Formulate and solve the main problems of control theory. 4. Apply methods of matrix theory. 4. Possession of: 1. Basic skills in programming and using application packages. 2. Skills of analysis and solving problems of mathematical modeling using algebraic approaches, methods of mathematical and functional analysis, and operations research.

The purpose of the discipline consists of teaching students theoretical and practical approaches to analysis with stability techniques. Mastering the general formulations and methods of solving applied problems of stability theory.

1. Bashniakov O.M., Pichkur V.V. Zadacha syntezu v teorii keruvannia: Navchalnyi posibnyk. – K.: Vyd-vo «Stal», 2012. – 116 s. 2. Demidovich B.P. Lekcii po matematicheskoj teorii ustojchivosti. – SPb.: Lan', 2008. – 480 s. 3. Harashchenko F.H., Pichkur V.V. Prykladni zadachi teorii stiikosti. – K.: VPTs «Kyivskyi universytet», 2014. – 142 s. 4. Samoilenko A.M., Perestiuk M.O., Parasiuk I.O. Dyferentsialni rivniannia. – K.: Lybid, 2003. – 600 s. 5. Khalil H.K. Nonlinear systems. – NJ.: Prentice Hall, 2002. – 766 p. 6. Pichkur V.V., Kapustian O.V., Sobchuk V.V. Teoriia dynamichnykh system. – Lutsk: Vezha-Druk, 2020. – 348 s. 7. Bashniakov O.M., Harashchenko F.H., Pichkur V.V. Praktychna stiikist, otsinky ta optymizatsiia. –K.: Kyivskyi universytet, 2008. – 383 s.

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

Semester assessment: The perfect score that can be obtained by a student is 60 points: 1. Test work №1: 20/12 points. 2. Test work №2: 20/12 points. 3. Independent work №1: 10/6 балів. 3. Current assessment: 10/6 балів. 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: 5 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) performed and timely passed 2 tests from the list of proposed works.

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