METHODS OF TEACHING STUDENTS MATHEMATICAL MODELING USING THE EXAMPLE OF STUDYING THE MOVEMENTS OF A PENDULUM

Morozov A. V., Bulekbayev D. A.

More than 50 years ago, an outstanding Soviet mathematician, academician L.S. Pontryagin, noted that the most important and interesting technical applications of ordinary differential equations are in the theory of oscillations and the theory of automatic control. He expressed his views on the theory and some of its technical applications in his wonderful book Ordinary Differential Equations. Unfortunately, in modern educational programs of higher education institutions, applied questions in the course of ordinary differential equations are often omitted due to time constraints. This harms the quality of technical education, as students' motivation to study weakens. This article presents a methodology for studying the most important applied problem - the motion of a pendulum performing forced oscillations in a vertical plane. The authors focus on the fundamental concepts of the theory of differential equations and justify the need to use a computer. This approach gives a certain completeness to learning and builds mathematical modeling skills. The authors are convinced that the triad of ordinary differential equations, a personal computer and a numerical experiment should be integrated into the educational process of universities to a greater extent than it is now.

Keywords:pendulum equation, phase plane, bifurcations, separatrices, teaching methods