Exercises
1. Fourier series

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 squarewave.

Graph the first approximation to the square
wave 2 sin(2 pi x)/pi.

Draw the approximation by 9 terms.
The nth term is (2/pi) sin (2 pi (2n1) x)/(2n1).

Now make a series of pages, amounting to
a simple animation.
2. Graphing integrals

Let F(x) be the definite integral of
cos t^{2} 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
and derivatives.)
3. Newton's method

Put together one or more figures that, briefly and all
by themselves, explain Newton's method for finding roots.
