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Applied problems of variational calculus

ДВС.2.01

Вибіркова дисципліна для ОП

First

2023/2024

6 Semester

5

LO 15. Be able to organize their activities and get results within a limited time. PLO 23.2. Be able to analyze independently the subject area and develop mathematical and structural-algorithmic models.

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. 2. Knowledge: 1) Theoretical basics of properties of differential equations solutions. 2) Principles of analysis and optimization of control systems. 3) Numerical methods for finding solutions to extreme problems. 3. Skills: 1) Solve the basic problems of the differential equations theory. 2) Do research on the properties of the extreme functions. 3) Form and solve the main problems of control theory. 4) Apply matrix theory methods. 4. Possession of: 1) Basic skills in programming and application packages. 2) Basic principles of solving linear systems of differential equations. 3) Skills of integration and differentiation of functions, finding the extremum of functions.

The purpose of the discipline consists of mastering the constructive approaches and methods of the calculus of variations by students. Studying the modern constructive methods of solving problems of discrete control systems. Learning the applied methods and problem statements.

1. Harashchenko F.H., Matvienko V.T., Pichkur V.V. & Kharchenko I.I. (2015). Dyferentsialni rivniannia, variatsiine chyslennia ta yikh zastosuvannia. K., VPTs «Kyivskyi universytet». 2. Bashniakov O.M. & Pichkur V.V. (2012). Zadacha syntezu v teorii keruvannia: Navchalnyi posibnyk. K.: Vyd-vo «Stal». 3. Bashniakov O.M., Harashchenko F.H. & Pichkur V.V. (2008). Praktychna stiikist, otsinky ta optymizatsiia. K.: Kyivskyi universytet. 4. Vasilev F.P. (2002). Metody optimizatsii. M.: Faktorial Press. 5. Perestiuk M.O., Stanzhytskyi O.M., Kapustian O.V. & Loveikin Yu.V. (2010). Variatsiine chyslennia ta metody optymizatsii. K.: VPTs «Kyivskyi universytet». 6. Aleksandrov V.V., Boltyanskiy V.G., Lemak S.S., Parusnikov N.A. & Tikhomirov V.M. (2005). Optimalnoe upravlenie dvizheniem. M.: Fizmatlit. 7. Bublik B.N. & Kirichenko N.F. (1975). Osnovy teorii upravleniya. K.: Vishcha shkola. 8. Mokliachuk M.P. (2003). Variatsiine chyslennia. Ekstremalni zadachi. K.: Lybid.

Lectures, off-class work, studying the literature sources recommended, homework.

Semester evaluation: The maximum score that can be received by a student is 60 points: 1. Control work №1: - 20/12 points. 2. Control work №2: - 20/12 points. 3. Off-class work № 1: - 10/6 points. 4. Off-class work № 2: - 10/6 points. Final evaluation (in the form of an exam): - Maximum score that can be received by a student: 40 points. - Form of performing: written test. - Types of tasks for each module: 2 written tasks (1 theoretical question and 1 practical task). - A student receives an overall positive grade in the discipline if his exam grade is not less than 24 (twenty-four) points. - A student is admitted to the exam if during the semester he (she): 1) scored at least 36 points; 2) performed and submitted according to the deadline 2 (two) off-class works from the list of suggested tasks.

Ukrainian