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Actual problems of applied mathematics

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

PLO1. Be able to use of in-depth professional knowledge and practical skills to optimize the design of models of any complexity, to solve specific problems of designing intelligent information systems of different physical nature.

1. Have competencies in: mathematical analysis, functional analysis, theory of differential equations, theory of optimal control, algebra and numerical methods. 2. Be able to: develop computer programs (proficiency with at least one programming language). Read and analyze mathematical texts, create own mathematical texts. Reading literature in English. 3. Have skills: working with a computer, searching for information on the Internet, using translation tools, creating mathematical texts and presentations.

The purpose of the discipline is to develop students' diverse and deep understanding of current approaches of applied mathematics related to the problems where it is actively used. As a result, the student must have competencies in research, improvement and development of methods of applied mathematics, in particular, aimed at the problems of optimal control, mathematical economics and the so-called incorrect problems. Within the discipline, students gain knowledge in relevant areas of applied mathematics research, develop skills necessary for researchers in the field, train to conduct and present the results of mathematical research and numerical modeling. Problems that arise in the construction, research and application of algorithms for mathematical modeling and optimal control problems are considered, in particular, when it is necessary to work with initially incorrect problems.

1. Lyashko S.I., Sandrakov H.V., Semenov V.V., Klyushin D.A. Matematychne modeliuvannia ta obchysliuvalna matematyka. Kyiv, VPTs “Kyivskyi universytet”, 2020 2. Lyashko S.I., Semenov V.V., Klyushin D.A. Spetsialni pytannia optymizatsii. Kyiv, VPTs “Kyivskyi universytet”, 2015 3. Sea Zh. Optymyzatsyia. Teoryia y alhorytmy. – M.: Myr, 1973. 4. Tykhonov A.N., Arsenyn V.Ya. Metody reshenyia nekorrektnykh zadach. – M.: Nauka, 1979. 5. Haevskyi Kh., Hryoher K., Zakharyas K. Nelyneinye operatornye uravnenyia y operatornye dyfferentsyalnye uravnenyia. – M.: Myr, 1978. 6. Yosyda K. Funktsyonalnyi analyz. – M.: Myr, 1967. 7. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston / Dordrecht / London: Kluwer Academic Publishers, 2002. 466 p. 8. Vasylev F.P. Metody reshenyia ekstremalnykh zadach. – M.: Nauka, 1981. 9. Nesterov Yu.E. Vvedenye v vypukluiu optymymzatsyiu. – M.: MTsNMO, 2010. ..

Lectures, independent work, work on own project.

- semester assessment: 1. Test 1 - 25 points / 15 points 2. Test 2 - 25 points / 15 points 3. Report presentation - 25 points / 15 points 4. Project presentation - 25 points / 15 points Final grade is based on the results of work in the semester. A student passes the course if he / she scores 60 or more on the results of the semester, and has successfully passed at least three forms of semester control.

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