Infopaket

Equations of mathematical physics

ННД.33

Обов’язкова дисципліна для ОП

First

2024/2025

8 Semester

3

PR 01. Know and be able to apply in practice differential and integral calculus, Fourier series and integrals, analytic geometry, linear algebra and vector analysis, functional analysis, and discrete mathematics to the extent necessary to solve typical problems of systems analysis. PR 04. Know and be able to apply basic methods of qualitative analysis and integration of ordinary differential equations and systems, differential equations in partial derivatives, including equations of mathematical physics. PR 09. Be able to create efficient algorithms for computational problems of systems analysis and decision support systems. PR 15. Understand Ukrainian and foreign languages ​​at a level sufficient for the processing of professional information and literature sources, and professional oral and written communication on professional topics.

Full-time form

For the successful study of the course “Equations of Mathematical Physics,” a student must meet the following requirements: Prerequisite courses: successful completion of Mathematical Analysis, Differential Equations, Algebra, Analytical Geometry. Knowledge: main topics of mathematical analysis, algebra, and analytical geometry. Skills: ability to find derivatives, compute integrals, analyze functions for extrema, solve systems of linear algebraic equations with parameters, and apply methods of matrix algebra. Competencies: ability to identify derivatives and antiderivatives of fundamental mathematical functions in various expressions; construct systems of algebraic equations; apply methods for finding polynomial roots; and use methods for analyzing qualitative characteristics of constructed mathematical models.

The aim of the course is to provide students with knowledge of the fundamental theoretical principles and methods for solving partial differential equations, approaches to solving initial-boundary value problems and Cauchy problems, the study of the correctness of boundary value problem formulations, and the acquisition of methods for constructing mathematical models of various physical processes in the form of boundary value problems for partial differential equations.

1. Perestiuk M.O., Marynets V.V. Teoriia rivnian matematychnoi fizyky.-Kyiv: «Lybid», 1993, 250 p. 2. Virchenko N.O. Osnovni metody rozviazannia zadach matematychnoi fizyky.- Kyiv, KPI, 1997, 370 p. 3. Dovhyi S.O., Lifanov I.K. Metod Synhuliarnykh intehralnykh rivnian. Teoriia ta zastosuvannia. - Kyiv, «naukova dumka», 2004, 510 p. 4. Dovgiy, S.O., Lyashko, S.I., Cherniy, D.I. Algorithms of the Discrete Singularity Method for Computing Technologies // Cybernetics and Systems Analysis, 53 (6). - 2017. - pp. 950-962. DOI: 10.1007/s10559-017-9997-4.

Lectures, practical classes, independent work, elaboration of recommended literature, homework.

The maximum number of points a student can obtain is 100 points: 1. Midterm test 1 (Part I): 30 points / 18 points. 2. Midterm test 2 (Part II): 30 points / 18 points. Continuous assessment: 40 points / 24 points. Final assessment: in the form of a credit test. It is based on the student’s performance throughout the semester and does not require additional assessment activities for students who have achieved satisfactory results.

Ukrainian