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Differential equations

ОК 5.

Обов’язкова дисципліна для ОП

First

2024/2025

2 Semester

5

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 the educational and qualification level "Bachelor of Physics" and is basic for studying all physical and some mathematical disciplines. The course program is focused on students who are already familiar with mathematical analysis and the basics of linear algebra. The learning outcomes consist of knowledge of the general properties of ordinary differential equations and their systems, formulation of differential problems and investigation of the stability of their solutions. It is important to develop skills in analyzing and solving standard types of differential equations that are typical of the laws of physics. Teaching methods: lectures, consultations, practical classes. Assessment methods: survey during practical classes, tests after the main sections of the course, exam. The final grade is given on the basis of intermediate grades (60%) and exam (40%).

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 - 45 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 assessment is conducted in the form of an exam (40 points). The final grade is the sum of the semester and exam grades.

Ukrainian