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Mathematical modeling ОК.16

ОК.16

Обов’язкова дисципліна для ОП

First

2024/2025

6 Semester

3

PLO 3. Formalize problem sets up in the language of a particular subject area; define their mathematical formulation and choose a rational problem-solving approach; solve the obtained problems with analytical and numerical methods, evaluate the accuracy and reliability of the results obtained. PLO 17. Be able to collect, process, analyze, systematize scientific and technical information, while avoiding academic dishonesty.

Distance form

1. Be able to formulate and solve initial-boundary value problems of mathematical physics, solve systems of linear algebraic equations, and master the methods of numerical differentiation and integration. 2. Possess skills in practical construction and software implementation of algorithms and methods of classical computational mathematics in solving applied problems.

The aim of the course is to master the principles of constructing mathematical models of spatially distributed dynamic processes and phenomena, as well as the mathematical modeling of their state under conditions of incomplete information about their external-dynamic state and the methods of controlling it. As a result of studying this course, the student should learn to understand the problems and be able to solve direct and inverse initial–boundary value problems of the dynamics of spatially distributed systems that are incorrectly formulated with respect to the quantity and quality of initial–boundary observations, and to master methods for their practical software implementation.

1. Stoyan V.A. Matematychne modeliuvannia liniinykh, kvaziliniinykh i neliniinykh dynamichnykh system. – K.: VPTS "Kyivskyi Universytet", 2011. – 320 p. 2. Stoyan V.A. Modeliuvannya ta identyfikatsiia dynamiky system z rozpodilenymy parametramy. – K.: VPTS "Kyivskyi Universytet", 2004. – 184 p. 3. Stoyan V.A. Osnovy laboratornoho modeliuvannya prostorovo rozpodilenykh dynamichnykh system. – K.: VPTS "Kyivskyi Universytet", 2017. – 118 p. 4. Stoian V.A. Laboratorne modeliuvannia prostorovo rozpodilenykh dynamichnykh system – K.: VPTs «Kyivskyi universytet», 2021. – 174 p. 4. Skopetskyi V. V., Stoyan V. A., Kryvonos Yu. H. Matematychne modeliuvannia priamykh ta obernenykh zadach dynamiky system z rozpodilenymy parametramy. – K.: Naukova dumka, 2002 – 361 p. 5. Skopetskyi V.V., Stoyan V.A., Zvarydchuk V.B. Matematychne modeliuvannia dynamiky rozpodilenykh prostorovo-chasovykh protsesiv. – K.: Stal, 2008. – 316 p.

Lectures, laboratory works, independent work.

Semester assessment: The maximum number of points that can be obtained by a student is 60 points: 1. Test work № 1 - 12/7 points. 2. Current assessment - 12/7 points. 3. Oral answers - 12/7 points. 4. Test work № 2 - 12/7 points. 5. Testing students' knowledge - 12/8 points. Final assessment in the form of an exam: - the maximum number of points that can be obtained by a student is 40 points; - form and types of tasks: written work. Types of tasks: 3 written tasks (2 theoretical questions of 10 points and 1 practical task - 20 points).

Ukrainian