Applied stability problems

Course: Applied Mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Applied stability problems
Code
ДВС.2.03
Module type
Вибіркова дисципліна для ОП
Educational cycle
First
Year of study when the component is delivered
2023/2024
Semester/trimester when the component is delivered
7 Semester
Number of ECTS credits allocated
23
Learning outcomes
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
Form of study
Full-time form
Prerequisites and co-requisites
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.
Course content
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.
Recommended or required reading and other learning resources/tools
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.
Planned learning activities and teaching methods
Lectures, classes, self-study, study of the recommended sources, homework.
Assessment methods and criteria
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.
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Volodymyr V. Pichkur
Complex systems modelling
Faculty of Computer Science and Cybernetics

Departments

The following departments are involved in teaching the above discipline

Complex systems modelling
Faculty of Computer Science and Cybernetics