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 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 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.