Abstract
Purpose. To show the possibilities of using mathematics software in solving problems arising in the construction of mathematical models of various processes and, thus, to reveal the importance of realizing the professional orientation of the mathematical training of students of natural and engineering specialties. Methodology. A number of mathematical models that are presented in the form of a Cauchy problem for a common first-order differential equation are considered in this paper. Mathematical models considered in this paper describe chemical and ecological processes. Euler's numerical method is used to solve the problems that describe the proposed models. This method is implemented in special mathematical software (Mathcad, Matlab). Findings. It is shown how the use of special functions designed to solve the Cauchy problem solves the problems proposed in mathematical models. Graphs are built in Mathcad and Matlab, including graphs that can be used to compare analytical and numerical solutions of problems obtained by Euler's method. Originality. The paper concludes that mathematical models of many technological and physical processes in different industries can be represented by the Cauchy problem for a common differential equation. Practical value. The considered mathematical models show the importance of realization of professional orientation of mathematical training of students of natural and engineering specialties. Conclusions. Mathematical modeling allows you to study and evaluate various processes (physical, economic, environmental), and therefore knowledge of the basics of modeling and special mathematical software is very important in the training of modern specialists in various specialties. The problems presented in the article are used in teaching the courses of numerical methods and computer mathematics in the study of the topic «Numerical Solution of Differential Equations». References 10, tables 2, figures 9.
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