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Numerical methods of stability and sensitivity

ДВС.2.08

Вибіркова дисципліна для ОП

First

2023/2024

8 Semester

4

LO 4. Be able to describe and analyze discrete objects and systems, using the concepts and methods of discrete mathematics and algorithm theory. LO 14. Demonstrate the ability to self-study and professional development. LO 18. Communicate effectively on information, ideas, problems, and solutions with professionals and society. PLO 23.2. Be able to analyze independently the subject area and develop mathematical and structural-algorithmic models.

Full-time form

To successfully study the discipline "Numerical methods of stability and sensitivity", a student must meet the following requirements: Knowledge: 1. Theoretical foundations and methods of construction, verification, and research of quantitative and qualitative properties of mathematical models. 2. Principles of analysis and optimization of control systems. 3. Numerical methods of finding solutions of differential equations and systems of differential equations. Skill: 1. To solve the basic problems of the theory of differential equations. 2. Research the properties of functions. 3. Formulate and solve the main problems of control theory. 4. Apply methods of matrix theory. Possession: 1. Basic programming skills and use of application program packages. 2. Skills of analysis and solving problems of mathematical modeling using algebraic approaches, methods of mathematical and functional analysis, and operations research.

Students mastery of theoretical and practical approaches to the analysis of solutions to stability and sensitivity problems. Mastering general statements and methods of solving applied problems of the theory of stability and sensitivity. The course includes 2 tests. The discipline ends with an exam.

1. Bashniakov O.M., Pichkur V.V. Zadacha syntezu v teorii keruvannia: Navchalnyi posibnyk. – K.: Vyd-vo «Stal», 2012. – 116 p. 2. Garashchenko F.H., Pichkur V.V. Prykladni zadachi teorii stiikosti. – K.: VPTs «Kyivskyi universytet», 2014. – 142 p. 3. Samoilenko A.M., Perestiuk M.O., Parasiuk I.O. Dyferentsialni rivniannia. – K.: Lybid, 2003. – 600 p. 4. Khalil H.K. Nonlinear systems. – NJ.: Prentice Hall, 2002. – 766 p. 5. Pichkur V.V., Kapustian O.V., Sobchuk V.V. Teoriia dynamichnykh system. – Lutsk: Vezha-Druk, 2020. – 348 p. 6. Bashniakov O.M., Harashchenko F.H., Pichkur V.V. Praktychna stiikist, otsinky ta optymizatsiia. – K.: Kyivskyi universytet, 2008. – 383 p. 7. Garashchenko F.H., Shvets O.F. Vstup do analizu chutlyvosti parametrychnykh system: Nachalnyi posibnyk – K.: VPTs «Kyivskyi universytet», 2006. – 115 p.

Lectures, seminar classes, independent work, study of recommended literature, homework.

Semester assessment: The maximum number of points that can be obtained by a student is 60 points: 1. Test work No. 1: 20/12 points. 2. Control work No. 2: 20/12 points. 3. Independent work No. 1: 10/6 points. 4. Current assessment: 10/6 points. Final evaluation (in the form of an exam): - The maximum number of points that can be obtained by a student: 40 points. - Form of conduct: written work. - Types of tasks: 4 written tasks (2 theoretical questions and 2 practical tasks). - The student receives an overall positive grade in the discipline if his grade for the exam is at least 24 (twenty-four) points. - A student is admitted to the exam if during the semester he: scored at least 36 points in total; and completed and passed 2 (two) test papers on time.

Ukrainian