Abstract:

The study of differential equations is an attractive illustration of the application of the ideas and techniques of calculus in our everyday live. Always, when we ask oneself the practical questions such as: “How fast does a given quantity change?”, “How long does a given quantity change?”, we come to the rate, speed and change quantities or generally derivation. Unfortunately, these techniques of calculus are not always easy and the students have a big problems with solving both the theoretical and practical examples, in which the solution of differential equations appears. Consequently, the aim of this paper is to show some simple practical applications which are suitable for teaching differential equations, not only in the study of the future transport engineers and highlight the most frequently occurring errors in their solutions. All applications will be solved not only exact, but it will be always compared a particular with numerical solutions. It will be also accompanied by a script in Matlab and the graphical comparison of the particular types of the solutions. The examples that are used in teaching of differential equations and numerical methods at Jan Perner Transport Faculty University of Pardubice will be used in this article and they can be used as an inspiration for teaching at the other universities with the same or the similar focus.

Keywords:

Differential equations, applied mathematics, errors, exact and numerical solution, comparison, Matlab.