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Methods of mathematical physics

ОК 18.

Обов’язкова дисципліна для ОП

First

2023/2024

4 Semester

4

Learning outcomes are knowledge of the basic equations of mathematical physics and problem statement for them, their physical interpretation in terms physical models. Students must master the basic methods of mathematical physics: the method of separation of variables, decomposition by eigenfunctions, integral Fourier and Laplace transforms, know basic special functions, their properties, and be able to apply them to solve equations in partial derivatives, master a concept of generalized functions and Green's functions of mathematical physics.

Full-time form

To know the properties of elementary functions, basic laws of mechanics, electrics, problem statement and methods for solving ordinary linear differential equations, expressions for the Laplace operator in cylindrical and spherical coordinate systems, vector differential operations. То be able to apply previous knowledge of mathematical analysis, vector and tensor calculus and differential equations, solve algebraic and differential equations and systems, decompose functions into power series. Possess skills in calculating derivatives, integrals, researching and plotting functions, application of methods of theory of functions of a complex variable, skills in the application of delta functions, gamma and beta functions.

The normative discipline "Methods of Mathematical Physics" is a component of the cycle of professional training of specialists of the educational and qualification level "Bachelor of Physics". It is the last general math course that completes the general math education of students, that provides a basis for the courses of electrodynamics, quantum mechanics and special disciplines. The course of methods of mathematical physics is designed to help students master the methods of mathematical physics as a tool of the analytical apparatus of physics, as well as to form a holistic system of knowledge and scientific thinking, and to consolidate previously acquired mathematical knowledge through their active use.

4. Yurachkivsky A.P., Zhugaevich A.Ya. Mathematical physics in examples and problems, K: Kyiv Univ. Press, 2005. 6. Dotsenko I.S., Yakimenko O.I. Methods of mathematical physics: a textbook for students of the Faculty of Physics. Kyiv: Kyiv University Press, 2007. 7. Perestyuk M.O. Theory of equations of mathematical physics: Textbook / M.O. Perestyuk, V.V. Marynets. Kyiv: "Lybid", 2006. 8. Virchenko N.O. Basic methods of solving problems of mathematical physics. K. KPI, 1997.

The total amount of 120 hours, including: Lectures - 30 hours. Practical classes - 30 hours. Independent work - 60 hours.

The control is carried out according to the module-rating system, which consists of 2 content modules. The knowledge assessment system includes current, modular and semester control of knowledge. Forms of current control: assessment of homework, written independent assignments, tests and tests performed by students at home and during practical classes. The student can get a maximum of 60 points for homework, independent assignments, oral answers, tests, additions to practical classes (30 points in each content module. Modular control: 2 modular tests. The student can get a maximum of 32 points for modular tests (12 and 20 points for the first and second work, respectively.) The final semester control is conducted in the form of a test (40 points).

Ukrainian