ВИКОРИСТАННЯ ПРОГРАМНИХ ЗАСОБІВ ПРИ ВИВЧЕННІ МЕТОДІВ МАТЕМАТИЧНОЇ ФІЗИКИ В БІОЛОГІЇ ТА МЕДИЦИНІ

Abstract

The questions of mathematical modeling of various phenomena and processes in various branches of biomedical engineering are considered. In the modern scientific environment considerable attention is paid to the methods of evidence-based medicine. For this purpose, specific mathematical models of objects and processes are used in the form of corresponding mathematical equations. The solution of these equations is an essential element of the evidence base in medicine and biology. Obtaining the very analytical solution is a significant value as proof. The development of methods of analytical solution of the problems of mathematical physics is a significant difficulty in the process of preparing non-mathematical students, therefore the use of software packages that provide such an opportunity is expedient and promising. In the educational process, in addition to lectures and practical classes, it is expedient to conduct laboratory and practical classes, where a student acquires a special software tool (Maple) and learns to apply it for solving mathematical problems, in particular problems of mathematical physics. In doing so, he must apply a series of sequential actions and algorithms.One of the first tasks in mathematical physics is the need to determine the type of existing equation and the possibility of obtaining an analytical solution. Different classes of equations of mathematical physics are considered for solving. Special attention is given to the construction of equations to the canonical form. In laboratory work, problems of greater complexity can be investigated in some limited space. These tasks are quite complex, and to solve them, it is usually necessary to apply methods of separating variables.The use of software tools for analytical solution of problems of mathematical physics in medicine and biology is considered appropriate for educational process and research activity and can be used for modeling phenomena and processes in various branches of biomedical engineering. This allows to create mathematical models of biophysical phenomena and study the effects of different initial and boundary conditions.