Infopaket

Differential Equations

ОК 25

Обов’язкова дисципліна для ОП

First

2021/2022

3 Semester

4

Basic methods of integration of the ordinary differential equations, solving of the initial value problem and the boundary value problem, basic methods of solving the system linear differential equation, basic principles and probable results of study of stability of the stationary states of dynamic systems, main features of the resonance in oscillating system.

Full-time form

To learn the “Differential equations” subject the second-year student must know those chapters of mathematical analysis and linear algebra, which are presented to the first-year students in the “Higher Mathematics” subject.

In the “Differential Equations” subject the basic methods of solving of the ordinary differential equations (both linear and nonlinear) and the systems of linear differential equations are explained. A special attention is paid to those mathematical concepts and objects, which are used not only for the solving of differential equations, in particular, to the integral Laplace transform, Dirac delta function, Green function. The basic points of the theory of oscillations and the stability theory for dynamic systems are explained in brief.

1. Львов В. А., Косогор А. О., Попадюк Д. Л. Просто про складне: звичайні диференціальні рівняння : навч. посіб.– К. : ВПЦ "Київський університет", 2022. 153 с. 2. Кривошея С. А., Перестюк М. О., Бурим В. М. Диференціальні та інтегральні рівняння. Київ : Либідь, 2004, 407 с. 3. Самойленко А. М., Кривошея С. А., Перестюк М. О. Диференціальні рівняння в задачах. Київ : Либідь, 2003, 395 с. 4. Головач Г. П., Калайда О. Ф. Збірник задач з диференціальних та інтегральних рівнянь. Київ : Техніка, 1997, 285 с.

Lectures, seminars, unsupervised work.

- Semester assessment. After each of two semantic modules the written test is carried out, the result of each test is scored from 0 to 30 points. -Final assessment. The written examination is carried out at the end of semester; the permit to examination is given if the subtotal result of two tests is no less then 30 points; examination test consists of 2 tasks and two problems, the performance of each task and solution of each problem is scored from 0 to 10 points. The result of learning of the subject is considered positive if the total score for semantic modules and exam exceeds 60 points, the score for exam must be higher than 20 points.

Ukrainian