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Mathematical study of the stability of fixed points of systems of differential equations describing biochemical processes rates
(Lutsk: LNTU, 2022-08-12) Hubal, Halyna
Mathematical study of the stability of fixed points of systems of differential equations describing biochemical processes rates is performed in the article. A system of differential equations for deviations is constructed, which describes the behavior of the system near the fixed point. An analysis of the general solution of the system of differential equations describing biochemical processes rates is made. The behavior of the systems near fixed points is investigated by the method of small perturbations. The conditions of existence of the limit cycle of the system of differential equations are investigated. For the cases when the system of differential equations cannot have an analytical solution, integrated curves are constructed by qualitative research. Phase trajectories of the system of differential equations describing biochemical processes rates are constructed. The definition of the nature of the stability of fixed points is considered and investigated.
Creating a course in probability theory and mathematical statistics in the Moodle system
(2026) Hubal, Halyna
This article develops a relevant direction in computer science – the creation of electronic educational courses in mathematical disciplines, in particular, a new approach to creating an electronic course in probability theory and mathematical statistics in the Moodle learning management system was proposed. The capabilities of the Moodle learning management system were analyzed when creating the course in probability theory and mathematical statistics. At the same time, the possibilities of implementing interactive tools of the Moodle learning management system were investigated. The structure of the course in probability theory and mathematical statistics was presented. Important interactive tools for assessing knowledge in the Moodle course were given: a test system and an assignment system. The combination of these two systems for assessing students' knowledge increases the efficiency of knowledge testing. New LaTeX source codes for problems were created in the Moodle system. The results of executing the LaTeX source codes in Moodle through the MathJax filter for rendering formulas in probability theory and mathematical statistics in a web browser were presented. The display of the formulas created by the LaTeX source codes has professional quality in any web browser on any platform and does not require the installation or configuration of additional software. In this article, it was recommended to use the interactive Forum tool and to add video lectures for a deeper understanding of the theoretical and practical material in the course in probability theory and mathematical statistics. It was shown that the Moodle learning management system allows to use advanced interactive tools when creating the course in probability theory and mathematical statistics to gain thorough knowledge and apply it in practical activities. This motivates students to conduct further scientific activities and to work in teams.
Credit-modular system as a tool for enhancing the quality of mathematical training in higher technical education institutions
(Київ: Наукові перспективи, 2026) Hubal, Halyna
In this article, the credit-modular system of organizing the educational process is considered as a tool for enhancing the quality of mathematical training of students at higher technical education institutions. The relevance of the investigation is caused by the need to optimize the mathematical training of students with increased requirements for learning outcomes, independent training of students, and objectivity in assessing the acquired knowledge in mathematical disciplines. The modular principle of the credit-modular system and the cumulative system of assessing students' knowledge were presented and analyzed. The modular principle of the credit-modular system, the cumulative system of assessing students' knowledge, and the specified requirements for learning outcomes create conditions for enhancing the quality of mathematical training of students in higher technical education institutions. In this article, it is shown that the use of a credit-modular system of organizing the educational process ensures flexibility and dynamism of the educational process, ensures the structured organization of the learning material, motivates students to constant educational activity, systematizing it, which is especially important for mastering mathematical knowledge. All this contributes to the individualization and intensification of the educational process in order to improve the assimilation of learning material. The results of the investigation justify the feasibility of further implementation and improvement of the credit-modular system during the mathematical training of students of higher technical education institutions. The results of the investigation may be useful for lecturers of mathematical disciplines at higher technical education institutions and for lecturers of other education institutions.
Automation of the creation of problems in mathematical analysis
(2026) Hubal, Halyna
In order to automatically create mathematical expressions for mathematical analysis, in particular mathematical expressions for the theory of limits, it is advisable to use the LaTeX programming language. In this article, the functionality of the LaTeX system was expanded to automatically create mathematical expressions for the theory of limits of mathematical analysis through programming methods using the LaTeX programming language. New commands were created. The created new commands accelerate the creation and updating of mathematical documents and provide flexibility in changing parameters. The created new commands can be used to prepare scientific publications and educational materials on mathematical analys.

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