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Equations of mathematical physics

ДВВ.11

Обов’язкова дисципліна для ОП

First

2021/2022

8 Semester

3

PR 01. Know and be able to apply in practice differential and integral calculus, Fourier series and integral, 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, professional oral and written communication on professional topics.

Full-time form

Тo successfully study the discipline "Equation of Mathematical Physics" the student must meet the following requirements: 1. Successful mastering of courses: 1. Mathematical modeling. 2. Optimization methods. 3. Variational calculus. 4. Differential equations. 5. Algebra. 6. Mathematical analysis. 2. Know: 1. fundamental bases of mathematical methods of construction, verification, research of qualitative characteristics of mathematical models. 2. principles of research of stationary, dynamic and computer models of control systems. 3. Be able to: 1. to study the qualitative characteristics of the constructed mathematical models. 2. formulate mathematical optimization problems for such models. 3. apply the considered methods for research of applied problems of modeling and optimal control. 4. Possess: 1. basic skills of using application packages for numerical analysis MATLAB and STATISTICA. 2. in English at a level not lower than Intermediate.

The purpose of the discipline is to master the methods of building mathematical models of various physical processes in the form of boundary value problems for partial differential equations, finding in analytical form solutions of certain types of boundary value problems and Cauchy problems, research the correctness of basic boundary value problems. The subject "Equations of Mathematical Physics" includes the study of various physical processes and their mathematical description, classification of second-order differential equations in partial derivatives, methods for solving initial-boundary value problems and Cauchy problems, for second-order differential equations in partial derivatives. Research of correctness of classical statement of boundary value problems. Such problems arise in physics, chemistry, biology, immunology, economics and other fields.

1. A.N. Тихонов, А.А. Samara Equations of Mathematical Physics. - М .:.: Наука, 1989. 2. S.G. Michlin Mathematical Physics Course. - M .: Nauka, 1968. 3. G.N. Positions Equations of Mathematical Physics M .: Higher School 1964. 4. A.B. Васильев, Н.А. Tikhonov Integral Equations, Moscow: Moscow University, 1989. 5. Dovgiy SA, Lifanov IK, Cherniy DI Method of singular integral equations and computational technologies.-K .: Publishing House "Euston" 2016, 380p. 6. DI Cherniy, and others. Methodical developments for the study of the normative course "Equations of Mathematical Physics". Kyiv -2001, - 65p. 7. В.П. Mikhailov Differential partial differential equations M .: Nauka, 1983. 8. O.A. Ladyzhenskaya Boundary value problems of mathematical physics M .: Nauka, 1973.

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

Semester assessment: Maximum number of points that can be obtained by a student: 60 points: 1. Test work №1: - 30/18 points. 2. Test work № 2: - 30/18 points. Final assessment (in the form of an exam): - Maximum number of points that can be obtained by a student: 40 points. - Form of conducting: written. - Types of tasks: 4 written tasks (2 theoretical questions and 2 practical tasks of 10 points).

Ukrainian