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Differential equations and numerical methods

ОК 15.

Обов’язкова дисципліна для ОП

First

2021/2022

1 Semester

6

To know and understand the basic concepts of metrology, measurement theory, mathematical and computer modeling, modern methods of processing and evaluating the accuracy of the measurement experiment. To understand the application of methods and techniques of analysis, design and research, as well as the limitations of their use. To be able to apply basic mathematical knowledge used in physics, optics and laser physics: analytical geometry, linear algebra, mathematical analysis, differential and integral equations, probability theory and mathematical statistics, methods of mathematical physics, theory of function of complex variables, mathematical modeling.

Full-time form

To know basic concepts of mathematical analysis and linear algebra. To be able to perform basic operations of integration and differentiation, calculation of limits, analyze the properties of functions, decompose functions into power series. To be able to operate by elementary methods of linear algebra, calculation of determinants, solving systems of linear equations

Ordinary differential equations of the first order. Cauchy's problem. Linear differential equations of order higher than the first. Linear boundary value problems, Sturm-Liouville problem. Systems of differential equations. Stability theory. Asymptotic methods for solving differential equations.

1. A.M. Samoilenko, S.A. Kryvosheya, M.O. Perestyuk, Differential equations in problems, K., Lybid, 2003. 2. S.A. Kryvosheya, M.O. Perestyuk, V.M. Burym, Differential and integral equations, K., Lybid, 2004. 3. Makarets, M.V., & Reshetnyak, V.Y. (1995). Ordinary Differential Equations and Calculus of Variations. 4. Momot A.I., Olikh O.Ya. Mathematical modeling. Practical lessons. Part 1. 5. P.P. Golovach, O.F. Kalaida, Collection of problems on differential and integral equations, K., 1997. 6. S.M. Yezhov Methods of calculations (K., Kyiv. University of Tet, 2001, 174 p.)

Lectures, practical classes, individual work.

Oral questioning during lectures and practical classes, homework, modul control work, exam.

Ukrainian