Infopaket

Differential equations

ОК.25

Обов’язкова дисципліна для ОП

First

2023/2024

3 Semester

6

PLO2. Use modern mathematical apparatus of continuous and discrete analysis, linear algebra, and analytical geometry to solve theoretical and applied problems in the design and implementation of informatization objects. PLO6. Use methods of numerical differentiation and integration, methods of ordinary differential and integral equations solving. Use features of numerical methods and apply them to solving engineering problems. Have skills in the software implementation of numerical methods.

Full-time form

To successfully study the discipline "Differential Equations", a student must meet the following requirements: 1. Successful completion of courses: 1. Mathematical analysis. 2. Algebra and geometry. 2. Knowledge: 1. Theoretical foundations of basic concepts of mathematical analysis, linear algebra, and operations research. 2. Principles of building mathematical models. Formalization of problem statements. 3. Skill: 1. Formulate and solve linear programming problems 2. Solve systems of linear algebraic equations with parameters. 3. Investigate functions at the extremum. 4. Ownership: 1. Basic skills in building, analyzing, and applying mathematical models when solving applied problems. 2. In English at the appropriate level. 3. Use packages of application programs for numerical analysis.

Familiarization with methods of solving various types of ordinary differential equations (ODEs), equations with partial derivatives, systems of differential equations, setting and solving Cauchy problems, familiarization with methods of modeling dynamic systems and studying their stability, familiarization with the basics of the calculus of variations for solving extreme problems. As a result of studying the academic discipline, the student should know basic concepts and definitions for the integration of scalar DRs and systems of ordinary DRs, linear DRs with partial derivatives, approaches to the analysis of singular points on the plane and the study of the stability of autonomous systems, statements and methods of solving the simplest variational problems. Be able to: solve integrated scalar DRs and systems of ordinary DRs, linear DRs with partial derivatives, conduct research on singular points and qualitative characteristics of constructed mathematical models, analyze stability, asymptotic stability, stability under constant disturbances of autonomous systems, solve the simplest variational problems. On the other hand, based on theoretical explanations, investigate problems that have an applied nature. Special attention is paid to the ability to develop numerical algorithms for stability analysis, obtain optimal estimates, and create software-algorithmic complexes for solving applied problems.

1. Garashchenko F.H., Matviienko V.T., Pichkur V.V., Kharchenko I.I. Dyferentsialni rivniannia, variatsiine chyslennia ta yikh zastosuvannia.. Navch. posib.. – K.: VPTs "Kyivskyi universytet", 2015. – 271 p. 2. Garashchenko F.H., Kharchenko I.I. Zbirnyk zadach i vprav z dyferentsialnykh rivnian. – K.: VPTs "Kyivskyi universytet", 2004. – 162 p. 3. Khusainov D. Ya., Bychkov O.S. Dyferentsialni rivniannia: Navchalnyi posibnyk. – K.: VPTs "Kyivskyi universytet", 2001. – 132 p. 4. Garashchenko F.H., Matviienko V.T., Kharchenko I.I. Dyferentsialni rivniannia dlia informatykiv. Pidruchnyk [z hryfom MON Ukrainy]. –VPTs „Kyivskyi universytet”, K., 2008. – 351 p. 5. Liashko I.I., Boiarchuk O.K, Hai Ya.H., Kalaida O.F. Dyferentsialni rivniannia. – K.: Vyshcha shkola, 1981. – 504 p. 6. Samoilenko A.M., Krivosheya S.A., Perestyuk N.A. Differentsialnie uravneniya. Primeri i zadachi. – K.: Vyshcha shkola, 1984. – 408 p.

Lectures, practical classes, independent work.

Semester assessment: 1. Control work 1: 25/15 points. 2. Control work 2: 25/15 points. 3. Verbal answers: 10/6 points. Final assessment (in the form of an exam): the maximum number of points that can be obtained by a student: 40 points. Form and types of tasks: written work.

Ukrainian