Infopaket

Differential equations and probability theory. Part one "Differential equations".

ОК 15

Обов’язкова дисципліна для ОП

First

2023/2024

3 Semester

4

The purpose of the discipline – student’s mastery of the basic concepts and methods of modern differential equations theory, learning the mathematical apparatus necessary for the studying of differential equations, as well as mastering the skills of applying knowledge in further education and professional activities.

Full-time form

Before studying the discipline of the first part of "Differential Equations and Probability Theory" it is necessary to prepare and pass exams in the following subjects: "Mathematical Analysis", "Algebra". Prerequisites: the student must know: complex numbers, basic methods of integration and differentiation, integration techniques, substitution of variables in differential expressions, methods of solving linear algebraic systems, methods of finding eigenvalues ​​and eigenvectors of a matrix, consept of ​​metric spaces. the student must be able to: use the mastered methods of differentiation and integration in practice in solving of differential equations, be able to solve some spesific problems from the courses "Mathematical Analysis" and " Algebra".

The discipline consists of three parts: 1. The first-order equations and methods for it’s solving: with separated variables and their modifications, linear, Bernoulli and Riccati equations, parameterization methods on the example of Lagrange and Clero equations, lowering methods in higher-order equations. 2. The theory of linear equations and systems, it’s properties. Equations with constant coefficients and variables, Abel's formula, Euler's method, method of variation of arbitrary constants, method of solution selection in the case when the right-hand side is a quasi-polynomial are considered. Linear systems are also considered: methods of exclusion and integrable combinations, Euler method for systems with constant coefficients, etc. 3. Additional aspects of the theory of differential equations: Lyapunov stability theory, operational method applied to equations and systems with constant coefficients, integral convolution-type equations, Sturm-Liouville problem, Green's function.

1). С.А. Кривошея, М. О. Перестюк, В. М. Бурим. Диференціальні та інтегральні рівняння. К., "Либідь", 2004. 2)С.А. Кривошея, Н.В. Майко, О.В. Сугакова Диференціальні рівняння: завдання для самостійної роботи студентів. ВПЦ «Київський університет», 2009. 3). А.М. Самойленко, С.А. Кривошея, М.О. Перестюк. Диференціальні рівняння в прикладах і задачах. К., "Либідь", 2003. 4). Г.П. Головач, О.Ф. Калайда. Збірник задач з диференціальних та інтегральних рівнянь. К., "Техніка", 1997 5) R.K. Nagle, E.B. Saff, A.D. Snider. Fundamentals of Differential Equations and Boundary Value Problems. Addison-Wesley, 2012

This course provides classes in the amount of: lectures - 30 hours, practical classes - 28 hours; independent work of students in the amount of 62 hours is also planned. Methods of semester control: tests conducted during practical classes and individual homework. Final control is exam.

Semester assessment: The academic semester has two meaningful modules. The first module is rated up to 35 points, the second - up to 25 points. Completion of individual homework is an integral part of the relevant module. Written tests are conducted after the completion of relevant topics. The course includes three current tests and two modular. Final assessment (in the form of an exam): the form of the exam is written-oral. The exam task consists of 2 theoretical questions and 3 problems. Each question and each problem is estimated from 0 to 8 points. In total, you can get from 0 to 40 points for the exam.

Ukranian