Infopaket

Differential equations

ННД.12

Обов’язкова дисципліна для ОП

First

2022/2023

3 Semester

9

LO 2. Be able to use basic principles and methods of mathematical, complex, and functional analysis, linear algebra and number theory, analytical geometry, and differential equations, including partial differential equations, probability theory, mathematical statistics and random processes, and numerical methods. LO 6. Be able to apply basic methods of building discrete and continuous mathematical models of objects and processes and analytical study of these models for the existence and uniqueness of their solution. LO 15. Be able to organize their activities and get results within a limited time.

Full-time form

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

Acquaintance and mastering methods of solving different types of ordinary differential equations, equations with partial derivatives, systems of differential equations, formulation and solution of Cauchy problems, stability research, and basics of the calculus of variations for solving extreme problems. The course includes 4 content parts and 4 control papers. In each semester, the discipline ends with an exam.

1. Khusainov D. Ya., Bychkov O.S. Dyferentsialni rivniannia: Navchalnyi posibnyk. – K.: VPTs «Kyivskyi universytet» 2001. – 132 p. 2. Khusainov D.Ya., Musatenko I.V. Dyferentsialni rivniannia: Navchalnyi posibnyk. – K.: VPTs «Kyivskyi universytet» 2001. – 132 p. 3. Garashchenko F.H., Matvienko V.T. Kharchenko I.I. Dyferentsialni rivniannia dlia informatykiv : Pidruchnyk. – K.: VPTs «Kyivskyi universytet» 2008. 4. Garashchenko F.H., Kharchenko I.I. Zbirnyk zadach i vprav z dyferentsialnykh rivnian. – K.: VPTs «Kyivskyi universytet» 2004. – 162 p. 5. Hudymenko F.S., Pavliuk I.A, Volkova V.O. Zbirnyk zadach z dyferentsialnykh rivnian. – K. Vyshcha shkola, 1972. –156 p. 6. Perestiuk M.O., Svishchuk M.Ya. Zbirnyk zadach z dyferentsialnykh rivnian: Navchalnyi posibnyk. – K.: Lybid, 1997. – 192 p.

Lectures, practical classes, independent work.

Semester evaluation: The maximum number of points that can be received by a student during the semester: 60 points: Control paper 1 from the first topic 20/12 points. Control work 2 on the second topic: 20/12 points. Current assessment: 20/12 points. Control paper 3 from the third topic: 20/12 points. Control paper 4 from the fourth topic 20/12 points. The current rating is 20/12 points. Final evaluation in the form of an exam: The maximum number of points that can be received by a student is 40 points. Form of conduct: written work. Types of tasks: 5 written tasks (2 theoretical questions and 3 practical tasks). A student receives an overall positive grade in the discipline if his grade for the exam is at least 24 points. A student is admitted to the exam if during the semester he: scored at least 36 points; and completed and on time passed at least 2 (two) control papers.

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