Demonstrations

On the day before fall break, I gave my Calculus II students an application of approximating integrals and series to finding the arclength of an ellipse. I was also able to provide a very gentle introduction to what a hypergeometric series is, and how they are useful for approximations. You can see my guided notes here.

I have also created several demonstrations for my Calculus II  class in the Desmos online graphing calculator inspired by examples in Stewart's textbook. I'm putting these here in case they will be useful to anyone else teaching the class.

The first example involves the cycloid introduced in 10.1 of Stewart. This curve is obtained by tracing the path of a point on circle with radius r as it rolls along the x-axis. This is illustrated below. As the parameter a varies, the green point on the circle traces out a cycloid.

I also illustrate how several parametric equations lead to beautiful graphs. The parameter b shows how the graph is traced out as t goes from 0 to 2 pi. There are several other complicated parametric equations that can be revealed by hiding and showing different graphs in Desmos.