Set up a figure 400 x 400 points.
Centre the coordinate system,
and choose a scale of 1 cm. Draw the axes.
Then draw a square-wave.
Graph the first approximation to the square
wave 2 sin(2 pi x)/pi.
Draw the approximation by 9 terms.
The n-th term is (2/pi) sin (2 pi (2n-1) x)/(2n-1).
Now make a series of pages, amounting to
a simple animation.
2. Graphing integrals
Let F(x) be the definite integral of
cos t2 from 0 to x.
(This is called the Fresnel integral.)
Graph F(x) for x = 0 to 24.
Use Simpson's rule and Bézier curves.
(Look at what the manual says about Bézier curves
3. Newton's method
Put together one or more figures that, briefly and all
by themselves, explain Newton's method for finding roots.