Abstract:

The formation of scientific concepts and their general theoretical systems acquires special significance in the context of a large-scale increase in the volume of scientific information and the intensification of knowledge. Formation of concepts in teaching is one of the forms of cognitive activity and theoretical thinking. Scientific concepts are interconnected and form a system of concepts.

This report is devoted to our experience in the formation of systems of concepts on dynamic systems (with the mandatory conduct of computer modeling) for undergraduate students studying in the specialty "Radio Engineering, Electronics and Telecommunications" of the Faculty of Physics and Technology Al-Farabi Kazakh National University. The concept of a dynamical system arose as a generalization of the concept of a mechanical system, the motion of which is described by Newton's differential equations. It covers systems of any nature: physical, chemical, biological, economic, pedagogical, etc. The description of dynamical systems also admits a great variety: it can be realized either by means of differential equations, or by means such as functions of algebra of logic, graphs, Markov chains, etc.

We consider dynamical systems described by nonlinear differential equations in ordinary derivatives. We use the mathematical model of a dynamic system based on the concept of a state, by which we mean the description of the system at some point in time, and the concept of an operator that determines the change of this state in time.

The first stage of studying dynamic systems is to consider the oscillations of a mathematical pendulum, electrical oscillations in the simplest circuit, made up of a capacitor and a coil. At this stage, the concepts of free and forced oscillations, a phase trajectory, a phase portrait, a linear and nonlinear oscillator are formed.

The second stage is the study of the self-oscillating system (using the example of the Van der Pol generator). Here we study such complex terms as the Poincare limit cycle, an attractor. We also show that self-oscillations in a dynamical system can be not only periodic, but also quasiperiodic and even stochastic.

The final third stage is the study of dynamical systems with chaotic behavior: Logistical Map, Lorenz system. We introduce the concepts of conservative and dissipative dynamical systems, the concept of chaos.

Each stage is accompanied by computer simulation in the MatLab system.

Thus, we have revealed that it is the formation of systems of concepts (not only individual concepts) that bind the intensification of the learning process, increase the integrity and integrativity of knowledge. Unification of concepts in the system contributes to the formation of a student's scientific outlook and experience of creative activity.

Keywords:

Undergraduate students, radio engineering, forming a system of concepts, dynamic system, nonlinear differential equations.