3D-Graphs

The examples below are not meant to be sophisticated. They should be thought of as a replacement for a blackboard drawing: instead of drawing a non-moving 3D-graph you would show an applet. You may think of it as the next step after showing a static picture with Powerpoint or using an old-fashioned slide.

These examples were made for the Analysis I/II course of D-BAUG and therefore are more relevant for service courses.

The applet below is an example from the first lesson on multidimensional differential calculus, where graphs of functions of two variables were defined, and partial derivatives and the notion of a tangent plane were introduced:

Here we’ve made a list of all the basic functions that we have studied in class, together with a list of all the notions that we have introduced. In the course book and in the related GeoGebraBook (see Chapter 3 of this text) we have provided the same applet, but with the possibility to input your favorite function:

This is what we have called a tailor-made computer algebra system (CAS) above; one can use applets as a CAS tailored for a specific goal.

Parametric Curves

In this topic, the students need a lot of help with visualization. Here is a good way to introduce the cycloid:

This very simple applet can be used in order to help the students understand the parametrization of the Epicycloid:

This applet is very useful for both the lectures and for the student as a CAS while working on the exercises: