Infopaket

Differential equations

ННД.24

Обов’язкова дисципліна для ОП

First

2023/2024

3 Semester

8

LO01. Know and be able to apply in practice differential and integral calculus, Fourier series and integrals, analytic geometry, linear algebra and vector analysis, functional analysis and discrete mathematics to the extent required to solve systems analysis typical problems. LO04. Know and be able to apply basic methods of qualitative analysis and ordinary differential equations and systems, differential equations in partial derivatives, including equations of mathematical physics, integration. LO06. Know and be able to apply the basic methods of setting and solving problems of system analysis in uncertainty of goals conditions, external conditions and conflicts. LO13. Design, realize, test, implement, maintain and operate software to work with data and knowledge in computer systems and networks. LO15. Understand Ukrainian and foreign languages at a level sufficient for processing professional information and literature sources, professional oral and written communication.

Full-time form

To successfully learn the discipline «Differential equations» the student's academic level must meet the following requirements: tо know: main sections on mathematical analysis, function optimization methods, algebra and analytical geometry; be able to: find derivatives, calculate integrals, investigate functions on extremum, solve systems of linear algebraic equations with parameters; to possess: matrix algebra methods, skills to notice derivatives and initials from basic mathematical functions in various mathematical expressions; compose algebraic equations systems; methods for calculating polynomials roots.

Familiarization with the basic theoretical positions and methods: ordinary differential equations and systems of differential equations solving; Cauchy problem and boundary value problem solving; stability investigation; variational calculus. The discipline belongs to the list of obligatory academic disciplines. The course is taught in 3rd and 4th semesters. It includes 4 semantic parts and 4 tests. The discipline ends with an exam in each semester.

1. Harashchenko F.G., Matviienko V.T., Pichkur V.V., Kharchenko I.I. Dyferentsialni rivniannia, variatsiine chyslennia ta yih zastosuvannia. – K.: VPTs «Kyivskyi universytet», 2016. – 250 s. 2. Elsgolts L.E. Differentsialnyie uravneniya i variatsionnoe ischislenie. – M.: Nauka, 1969. – 424 s. 3. Krasnov M.L. i dr. Obyiknovennyie differentsialnyie uravneniya: Zadachi i primery s podrobnymi resheniyami. – M.: Editorial URSS, 2002. – 256 s. 4. Hudymenko F.S., Pavliuk I.A, Volkova V.O. Zbirnyk zadach z dyferentsialnykh rivnian. – K.: Vyshcha shkola, 1972. – 156 s. 5. Filippov A.F. Sbornik zadach po differentsialnym uravneniyam. – M.: Nauka, 1992. – 128 s. 6. Samoilenko A.M., Krivosheia S.A., Perestiuk M.O. Dyferentsialni rivniannia v zadachakh. – K.: Lybid, 2003. – 504 s. 7. Charlz G. Edvards, Devid E. Penni. Differentsialnyie uravneniya i kraevyie zadachi. Modelirovanie i vychislenie s pomoschyu Mathematica, Maple i MATLAB. – M: OOO ID «Vilyams», 2008. – 1104 s.

Lectures, practical classes, independent work.

Assessment during the semester: The maximum number of available points is 60. Test no 1 on the first topic – 20/12 points. Test no 2 on the second topic – 20/12 points. Сurrent evaluation – 20/12 points. Test no 3 on the third topic – 20/12 points. Test no 4 on the fourth topic – 20/12 points. Сurrent evaluation – 20/12 points. Final assessment in the exam form: The maximum number of available points is 40. Form in which exam is taking: written work. Types of tasks: 5 written tasks (2 theoretical questions 8 points each; 3 practical tasks 8 points each). Exam tasks correspond to lectures and practical classes topics in accordance with semester. Tasks of tests correspond to the practical classes’ content of the according part.

Ukrainian