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Equations of mathematical physics

Обов’язкова дисципліна для ОП

First

2023/2024

5 Semester

8

LO 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. LO 6. Be able to apply basic methods of building discrete and continuous mathematical models of objects and processes, analytical study of these models for the existence and uniqueness of their solution. PLO 23.1. Be able to use professional knowledge, skills and abilities in the field of computational mathematics and computer science to model real processes of different nature.

Full-time form

1. Know: the basic concepts of algebra, mathematical analysis, differential equations, functional analysis at the basic level (the volume of the first and second courses of the university specialty Applied Mathematics). 2. Be able to: differentiate, integrate, investigate the convergence of series and improper integrals, solve and investigate systems of linear algebraic equations, ordinary differential equations. 3.Have basic skills: working with a computer, searching for information on the Internet, using translation systems

Module 1. Fredholm integral equations of the second kind, Sturm-Liouville problem. Lectures - 12 h, practical - 12 h, independent work - 28 h. Fredholm's theorems. Integral equations with a Hermitian nucleus. The Sturm-Liouville problem. Module 2. Mathematical models of physical processes. Statement of boundary value problems. Lectures - 14 h, practical - 14 h, independent work - 36 h. Heat and diffusion models. Models of elasticity. Perfect fluid models. Models of electrostatics and magnetostatics. Classification of equations in partial derivatives. Statement of problems of mathematical physics. Module 3. Methods for solving boundary value problems (BVP). Lectures - 18 h, practical - 22 h, independent work - 40 h. Methods for constructing solutions of BVP. Harmonic functions. Potential theory for the study of BVP. Generalized solutions of BVP. Module 4 Generalized solutions of boundary value problems. Lectures - 8 h, practical - 6 h, independent work - 24 h.

1. V.S. Vladimirov Uravneniya matematicheskoy fiziki. – M.: Nauka, 1981. 2. S.G. Mihlin Kurs matematicheskoy fiziki. – M.: Nauka, 1968. 3. A.N. Tihonov, A.A. Samarskiy Uravneniya matematicheskoy fiziki. – M.: 4. A.B. Vasilev, N.A. Tihonov Integralnyie uravneniya, M.: Moskovskiy unIversitet, 1989. 5. A.V. Kuzmin Konspekt kursu lektsIy RIvnyannya matematichnoYi fIziki http://195.68.210.50/moodle. 6. G.N. Polozhiy Uravneniya matematicheskoy fiziki M.: Vyisshaya shkola 1964. 7. V.P. Mihaylov Diferentsialnyie uravneniya v chastnyih proizvodnyih M.: Nauka, 1983. 8. O.A. Ladyizhenskaya Kraevyie zadachi matematicheskoy fiziki M.: Nauka, 1973. 9. V.S. Vladimirov Sbornik zadach po uravneniyam matematicheskoy fiziki. M.: Nauka, 1986. 10. B.M. Budak, A.A. Samarskiy, A.N. Tihonov Sbornik zadach po matematicheskoy fizike, M.: Nauka, 1972.

Lectures, independent work, recommended literature processing, homework.

5 semester Semester assessment: Maximum number of points that can be obtained by a student: 100: 1.Test 1: PH 1.1, PH 2.1 - 20 / 11 pts. 2.Test work 2: PH 1.1, PH 1.3, PH 2.1 - 20 / 11 pts. 3.Colloquium 1 PH 1.1, PH 1.3, PH 2.1 - 20 / 11 pts. 4.Homework check - 20 / 11 pts. 5.Work on practical classes - 20 / 11 pts. Final assessment (in the form of a test): 6 semester Semester assessment: Maximum number of points that can be obtained by a student: 60: 1.Test 1: PH 1.1, PH 2.1 - 15 / 9 pts. 2.Test work 2: PH 1.1, PH 1.3, PH 2.1 - 15 / 9 pts. 3.Colloquium 1 PH 1.1, PH 1.3, PH 2.1 - 15 / 9 pts. 4.Work on practical classes - 15 / 9 pts. Final assessment (in the form of an exam): Maximum number of points: 40. 1.Learning outcomes to be evaluated: PH1.1, PH1.2, PH1.3, PH1.4, 2.1, PH2.3; 2.Form of conducting and types of tasks: written with defense of the answer, 10 theoretical questions (2 p. for each) and two practical tasks (10 p. each).

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