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Title of discipline

Equations of mathematical physics

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Course of teaching

4, specialty 1-31 03 01-02 Mathematics (scientific and pedagogical activity)

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Semester of teaching

7

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Number of credits

4

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Full name of lecturer

Professor Yurchuk Nikolai Iosifovich

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Objectives of the study disciplines

The aim of discipline is to teach students to master the basic concepts of the theory of partial differential equations, mathematical methods of research and solving of the basic boundary value problems of mathematical physics.

As a result of the study, the student should be able to:

• investigate the correctness of the basic boundary-value problems for equations of mathematical physics;
• use the method of separation of variables to solve mixed problems for the basic equations of mathematical physics.

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Prerequisites

Mathematical analysis, ordinary differential equations.

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Content of discipline

Solving of initial-boundary value problems for the heat equation by the Fourier method. Solving of the Cauchy problem for the inhomogeneous heat equation. The maximum principle for the heat equation and its consequences. Integral representation of solutions of Poisson equation. Basic properties of harmonic functions. Green’s function of Dirichlet problem for Laplace equation. The study of methods for solving boundary value problems for elliptic equations.

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Recommended literature

1. Tikhonov A.N., Samarskii A.A. Equations of Mathematical Physics. Moscow, 1977.
2. Korzyuk V.I. Equations of Mathematical Physics. Minsk, 2011.
3. Lomovtsev F.E. Ломовцев Ф.Е. Equations of Mathematical Physics. Collection of tasks. Minsk, 2009.

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Teaching Methods

Problematic, communicative with elements of educational and research activity, controlled independent work.

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Language of teaching

Russian

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Conditions (requirements), actual control

• tests papers
• colloquiums

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Form of current certification

Exam