Infopaket

Differential equations and numerical methods

ОК 35.

Обов’язкова дисципліна для ОП

First

2023/2024

3 Semester

4

Learning outcomes are the knowledge of basic methods of analysis and solution of basic types of differential equations, in particular, linear equations and first-order systems, problems with boundary conditions (Sturm-Liouville problem), problems for constructing Green's function, setting differential problems, and studying their stability solutions, possession of elementary approximate methods of decomposition into power series and asymptotic series on a small parameter. It is important to develop skills for the self-development of algorithms for the implementation of various mathematical models that occur in practice. Ability to analyze and estimate computational errors. Knowledge of the practical application of numerical methods for obtaining results in theoretical models and for analysis of experimental data.

Full-time form

Students have to know the basics of mathematical analysis and linear algebra, in particular, be able to perform basic operations of integration and differentiation. They have to be able to apply elementary methods of solving differential and transcendental equations and know the basics of the C programming language.

The normative discipline "Differential equations and numerical methods" 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 disciplines. It is important to develop skills in analyzing and solving standard types of differential equations that are typical of the laws of physics. Computational methods are important for the study of theoretical and experimental physics in mathematics, which is the basis for the use of computer technology in the natural sciences to solve modern problems. Methods of numerical analysis, basics of writing algorithms for approximate calculations, and implementation in the form of computer programs are described. Methods of interpolation and approximation, solution of transcendental and differential equations, approximate operations of analysis with functions are considered as typical numerical problems.

1. S.M. Yezhov, Methods of Calculation, K. `` Kyiv University '', 2000. 8. V.V. Stepanov Course of differential equations. Kyiv, Soviet School, 1953, 444 p. 11. A.M. Samoilenko, S.A. Krivosheya, M.O. Perestyuk. Differential equations in examples and problems. Kyiv, Lybid, 2003, 395 p.

Lectures - 29 hours, practical classes - 56 hours.

Differential equations: The results of students' learning activities are evaluated on a 100-point scale. Forms of current control: assessment of written independent tasks, tests performed by students during practical classes. The student can receive a maximum of 30 points for homework, independent assignments, oral answers, additions to practical classes, tests (15 points in each content module). Modular control: 2 modular control works. Numerical methods: control is carried out by a modular rating system, which consists of 2 content modules. The knowledge assessment system includes current knowledge control. The student can receive a maximum of 30 points for individual tasks (15 points for each module). The final semester control is conducted in the form of an exam (40 points), the final grade is the sum of two semesters for practical classes on differential equations and numerical methods and examination grade.

Ukrainian