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Basics of nonlinear dynamics

ОК.14

Обов’язкова дисципліна для ОП

Second

2023/2024

2 Semester

6

PLO2. Understanding of the principles and methods of analysis and evaluation of the range of tasks that contribute to the further development of effective use of information resources.

Full-time form

1. Know chapters of mathematical analysis, basic concepts from the courses of ordinary differential equations, equations of mathematical physics, differential equations and algebra, elements of matrix analysis. 2. Be able to: carry out a qualitative study of ordinary differential equations on the plane and in three-dimensional space, investigate scalar differential equations and equations on the plane, investigate functions and functionals at the extremum, calculate eigenvectors and eigennumbers, find inverse matrices, reduce the matrix to the Jordan form, solve systems of linear inhomogeneous equations. 3. Possess the skills of elementary programming, use of mathematical packages of application programs, and numerical and analytical solutions of applied problems.

The goal of the discipline is to teach students of applied mathematics the ability to study mathematical models of nonlinear dynamic systems described by systems of ordinary differential equations, partial differential equations, and differential equations, to develop theoretical and practical abilities in this direction. The course includes 2 content parts and 2 control papers. The discipline ends with an exam.

1. Khusainov D.Ya., Shatyrko A.V. Osnovy neliniinoi dynamiky: Navchalnyi posibnyk Kyiv: VPTs «Kyivskyi universytet», 2017. – 159 p. 2. Chueshov I.D. Vvedenie v teoriyu beskonechnomernikh dissipativnikh sistem. – Kharkov, AKTA, 1999. – 436 p. 3. Sharkovskii A.N., Maistrenko Yu.A., Romanenko Ye.Yu. Raznostnie uravneniya i ikh prilozheniya. – Kiev: Naukova dumka, 1986. – 280 p. 4. Shatyrko A., Khusainov D. On the Interval Stability of Weak-Nonlinear Control Systems with Aftereffect // Open Source Journal. The Scientific World Journal, vol. 2016, Article ID 6490826, 8 pages, 2016. 5. Khusainov, D.Ya., Diblik, J., Bashtinec, Ja., Shatyrko, A.V. Investigating dynamics of one weakly nonlinear system with delay argument // Journal of Automation and Information Sciences – 2018, 50(1), p. 20-38.

Lectures, seminars, independent work

Semester evaluation: The maximum number of points that can be obtained by a student is 60 points. 1. Control work No.1: 20/12 points. 2. Control work No. 2: 20/12 points. 3. Current assessment: 20/12 points. Final evaluation in the form of an exam. The maximum number of points that can be obtained by a student is 40 points. Form of conduct: written work. Types of tasks: (2 theoretical questions and 1 practical task based on theoretical material). 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 in total; and completed and passed 2 (two) test papers on time.

Ukrainian