Infopaket

Differential equations

Обов’язкова дисципліна для ОП

First

2021/2022

3 Semester

8

Know the methods of solving first-order DRs, solved and unsolved in relation to the derivative. Know the mathematical methods of solving DRs of higher orders and boundary value problems. Know the methods of solving systems of ordinary differential equations and study the stability of their solutions and formulate basic theorems. Know the methods of solving first-order linear equations with partial derivatives and study of functionals to the extreme. Be able to correctly use the methods of DR theory in the problems of mechanics, biology, economics, control, choose a systematic approach to building dynamic models. Be able to correctly apply the methods of differential equation theory to solve applied problems. Substantiate your own view of the problem, communicate with colleagues on problem solving, compile written reports. Organize your independent work to achieve results.

Full-time form

To successfully study the discipline "Differential Equations" the academic level of the student must meet the following requirements: 1. Know: the main sections of mathematical analysis, methods for optimizing functions, algebra and analytical geometry. 2. Be able to: find derivatives, calculate integrals, investigate functions on the extremum, solve systems of linear algebraic equations with parameters, have methods of matrix algebra. 3. Have: skills to notice derivatives and primitives of basic mathematical functions in various mathematical expressions; compose systems of algebraic equations; methods for calculating the roots of polynomials.

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 "Differential Equations" is part of the educational and professional training program for bachelor's degree in higher education 12 Information Technology in the educational and professional program "Systems Analysis". The discipline belongs to the list of obligatory academic disciplines. It is taught in the 3rd and 4th semesters in the amount of 240 hours - 120 hours in the 3rd and 120 hours in the 4th semester (8 ECTS credits). In particular, lectures - 28 and 28 hours, respectively; consultations - 2 hours and 0 hours; practical classes - 28 and 28 hours, respectively; independent work - 62 and 64 hours. The course includes 4 substantive parts and 4 tests. Each semester the discipline ends with an exam.

1. Garaschenko F.G., Matvienko V.T., Pichkur V.V., Harchenko I.I. Diferentsialni rivnyannya, variatsiyne chislennya ta yih zastosuvannya. – K.: VPTs «Kiyivskiy universitet», 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 primeryi s podrobnyimi resheniyami. – M.: Editorial URSS, 2002. – 256 s. 4. Gudymenko F.S., Pavlyuk I.A, Volkova V.O. Zbirnik zadach z diferentsialnih rivnyan. – K.: Vischa shkola, 1972. – 156 s. 5. Filippov A.F. Sbornik zadach po differentsialnyim uravneniyam. – M.: Nauka, 1992. – 128 s. 6. Samoylenko A.M., Krivosheya S.A., Perestyuk M.O. Diferentsialni rivnyannya v zadachah. – K.: Lybid, 2003. – 504 s. 7. Charlz G. Edvards, Devid E. Penni. Differentsialnyie uravneniya i kraevyie zadachi. Modelirovanie i vyichislenie 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