Abstract:

This study directly follows on the article dealing with first order differential equations, published at ICERI 2016 conference. The study of second-order 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 second-order 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 exactly, in addition, comparison of a particular solution with a numerical solutions will be always shown. It will be also accompanied by a script in Matlab and the graphical comparison of the particular types of the solutions. The examples used in teaching of second-order 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 similar focus.

Keywords:

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