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Differential equations

ОК 21.

Обов’язкова дисципліна для ОП

First

2023/2024

2 Semester

2

Learning outcomes are knowledge of the general properties of ordinary differential equations of the first order and linear differential equations of higher orders. It is important to develop skills in analyzing and solving standard types of differential equations that are typical of the laws of physics.

Full-time form

Students have to know the basics of mathematical analysis and linear algebra. In particular, they have to be able to perform basic operations of integration and differentiation, calculation of limits, analyze the properties of functions, decompose functions into power series, apply previous knowledge of mathematical analysis, linear algebra to solve algebraic and transcendental equations. They must know basic methods of linear algebra for calculating determinants, solving systems of linear equations.

The normative discipline "Differential Equations" is a component of the cycle of professional training of specialists of educational and qualification level "Bachelor of Physics" and basic for the study of all physical and part of mathematical disciplines. The course program is aimed at students who are already familiar with mathematical analysis and the basics of linear algebra. The course is devoted to the presentation of elementary methods of integration of different types of differential equations of the first order and linear differential equations of higher orders, which are typical for physical problems.

2. V.V. Stepanov, Course of differential equations. Kyiv, Soviet School, 1953, 444 p. 5. A.M. Samoilenko, S.A. Krivosheya, M.O. Perestyuk. Differential equations in examples and problems. Kyiv, Lybid, 2003, 395 p.

Lectures - 30 hours, practical classes - 30 hours, independent work - 60 hours, consultations.

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 written independent tasks, tests performed by students during practical classes. The student can receive a maximum of 60 points for homework, independent assignments, oral answers, additions to practical classes (30 points in each content module). Modular control: 2 modular control works. The student can receive a maximum of 30 points for modular test work (15 points for each work). The final semester control is conducted in the form of a test (40 points). The final grade is the sum of semester and credit.

Ukrainian