Synergetics and mathematical modeling: integration of physical problems into the process of mathematical training of technical specialists

Abstract

The work is devoted to the urgent problem of improving the quality of fundamental mathematical training of future technical specialists in the conditions of dynamic development of science and technology. This contributes to the nonlinear interaction of mathematical and physical knowledge, the formation of a holistic system of scientific worldview. The article substantiates the theoretical and methodological principles of implementing the synergistic approach as an effective strategy for modernizing the educational process in higher technical educational institutions. From the standpoint of synergetics, fundamental mathematical training is considered as a complex, open pedagogical system that is in a state of nonlinear dynamics and self-organization. The key mechanism for implementing the synergistic approach in the article is the integration of solving physical problems into the process of studying higher mathematics. The work reveals the didactic potential of physical problems as a means of fundamentalizing mathematical training. The theoretical and didactic principles for implementing the synergistic approach in the fundamental mathematical training of future technical specialists by solving physical problems are determined; The article presents criteria for selecting and constructing physical problems integrated into a mathematics course, which ensure the formation of not only mathematical knowledge, skills and abilities, but also professionally oriented competencies, including skills in mathematical modeling, analysis of complex systems, problem-solving thinking, and interdisciplinary integration. The article provides an example of the implementation of the proposed approach in the mathematical training of future technical specialists.