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Equations of mathematical physics. Part 2

ННД.18.02

Обов’язкова дисципліна для ОП

First

2022/2023

6 Semester

4

LO 10. To know the methods of choosing rational methods and algorithms for solving mathematical problems of optimization, operations research, optimal management and decision-making, data analysis.

Full-time form

1. Know: the basic concepts of algebra, mathematical analysis, differential equations, functional analysis at the basic level (the scope of the first and second courses of the university). 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. Possess elementary skills: working with a computer, searching for information on the Internet, using translation systems.

Content module 3. Methods of solving boundary value problems of mathematical physics, correctness research. 13 Topic 13. Methods of constructing solutions of boundary value problems and Cauchy problems for classical boundary value problems of mathematical physics 14 Topic 14. Harmonic functions and their properties, Helmholtz equations, cylindrical functions and their applications. 15 Topic 15. Theory of potentials for the Laplace and Helmholtz operators for two-dimensional and three-dimensional cases 16 Topic 16. Use of potential theory to study boundary value problems of the Laplace and Helmholtz equations. Modular control work No. 3 17 Topic 17 Theory of potentials for the heat conduction equation. Content module 4. Generalized solutions of boundary value problems. 18 Topic 18. Mathematical apparatus for the study of generalized solutions of boundary value problems 19 Topic 19. Generalized solutions of boundary value problems for linear elliptic equations 20 Topic 20. Generalized solutions of boundary value problems for equations of parabolic and hyperbolic types. Colloquium No. 2 Control work No. 4

1. V.S. Vladimirov Uravneniia matematicheskoi fiziki. – M.: Nauka, 1981. 2. S.G. Mikhlin Kurs matematicheskoi fiziki. – M.: Nauka, 1968. 3. A.N. Tikhonov, A.A. Samarskii Uravneniia matematicheskoi fiziki. – M.: 4. A.B. Vasil-ev, N.A. Tikhonov Integral-nye uravneniia, M.: Moskovskii unіversitet, 1989. 5. A.V. Kuz-min Konspekt kursu lektsіi Rіvniannia matematichnoї fіziki http://195.68.210.50/moodle. 6. G.N. Polozhii Uravneniia matematicheskoi fiziki M.: Vysshaia shkola 1964. 7. V.P. Mikhailov Diferentsial-nye uravneniia v chastnykh proizvodnykh M.: Nauka, 1983. 8. O.A. Ladyzhenskaia Kraevye zadachi matematicheskoi fiziki M.: Nauka, 1973. 9. V.S. Vladimirov Sbornik zadach po uravneniiam matematicheskoi fiziki. M.: Nauka, 1986. 10. B.M. Budak, A.A. Samarskii, A.N. Tikhonov Sbornik zadach po matematicheskoi fizike, M.: Nauka, 1972.

Lectures, practical, independent work

- semester assessment: 1. Control work 1: RN 1.1, RN 2.1 — 15 points/9 points. 2. Control work 2: RN 1.1, RN 1.3, RN 2.1 – 15 points/ 9 points. 3. Colloquium 1 PH 1.1, PH 1.3, PH 2.1 – 15 points/9 points. 4. Work in practical classes - 15 points/9 points. - final evaluation (in the form of an exam)

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