Application of Ordinary Differential Equations - Modeling and Visualization

Ordinary differential equations are an essential part of core mathematical training in the field of technical studies. To highlight the importance of differential equations in natural and technical sciences, it is important to introduce students to possibility of modeling by using differential equations. The concept of modeling can be further clarified to students by using different computer visualization software packages. In the paper, this approach was illustrated by the modeling of the harmonic oscillator and the problem of pollution monitoring. The software package used was Wolfram Mathematica. It has been shown that computer visualization is a convenient method for checking, discussing and generalizing results. The resulting simplified models are then used to describe more complex situations. This approach to the problem of modeling not only enhances students' interest, but also improves their insight into the comprehensive use of mathematical tools and programming.