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Equations of mathematical physics. Part 1

ННД.18.01

Обов’язкова дисципліна для ОП

First

2023/2024

5 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: basic concepts of algebra, mathematical analysis, differential equations, functional analysis at the basic level (volume of the first and second courses of the university). 2. To be able to: differentiate, integrate, investigate the convergence of series and non-proper series integrals, solve and investigate systems of linear algebraic equations, ordinary differential equations. 3. Possess elementary skills: working with a computer, searching for information in Internet, use of translation systems.

Content module 1. Fredholm integral equations of the second kind, basic properties, Sturm-Liouville problem 1 Topic 1. Subject and method of discipline. The method of successive approximations for finding solutions of Fredholm integral equations of the second kind with continuous and polar kernels 2 Topic 2. Fredholm theorems for degenerate, continuous and polar nuclei, proof of theorems 3 Topic 3. Integral equations with a Hermitian kernel, Hilbert-Schmidt theorem. 4 Topic 4. The Sturm-Liouville problem and its connection with integral equations with a Hermitian continuous kernel. 5 Topic 5. Fredholm's integral equations of the first kind Content module 2 Mathematical models of physical processes, formulation of basic boundary value problems 6 Topic 6. Mathematical models of heat distribution and substance diffusion 7 Topic 7. Mathematical models of the theory of elasticity 8 Topic 8. Mathematical models of movement of an ideal fluid 9 Topic 9. Mathematical models of the movement of a viscous liquid 10 Topic 10. Mathematical models of electrostatics and magnetostatics 11 Topic 11. Classification of equations in partial derivatives 12 Topic 12. Formulation of classical problems of mathematical physics. Generalized functions and actions on them

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: First semester 1. Control work 1: RN 1.1, RN 2.1 — 20 points/11 points. 2. Control work 2: RN 1.1, RN 1.3, RN 2.1 – 20 points/11 points. 3. Colloquium 1 RN 1.1, RN 1.3, RN 2.1 – 20 points/11 points. 4. Homework check - 20 points/11 points. 5. Work in practical classes - 20 points/11 points. - final evaluation (in the form of credit)

Ukrainian