Fifth Central- and Eastern European Conference
on Computer Algebra- and Dynamic Geometry Systems
in Mathematics Education

Delays can appear in many phenomena in the Nature, and hence delay systems appear in many fields of Sciences. Their mathematical theory is quite new. Since understanding needs deep mathematics, hence only advanced courses deal with delay systems in mathematical curricula. On the other hand, undergraduate math and even science students should have a first impression of delay systems.

In our talk, we consider the didactic problems of teaching delay systems to students without or partly having the required knowledge. We present a short easy-to-understand visual way of introducing delay systems with the help of series of dynamic demonstrations developed in Mathematica. The basic concepts, properties, the difference between systems without and with delay are treated via elementary examples. We also give applications appearing in engineering and sciences.

The interactive demonstrations will be available on our website www.model.u-szeged.hu.

This paper presents the problems based on the examining functions and their properties with the use of derivative. The main idea is to analyze function and its derivative without using their analytical expressions. The package Geogebra is used for presenting visualized problems.

Key words: graph, function, derivative of function, visualized problems, cognitive-visual approach