This demonstration illustrates the use of Fourier series to represent functions. There are two functions built in. One is a step function. The display starts with the exact function. The first time you click the "Add a term button" the first term in the Fourier expansion is plotted. Each successive time you click the "Add a term button", another term is added from the Fourier series and the resulting approximation is plotted.

Notice that as you add terms the approximation gets better and better, though for the step function, the approximation is not so good near the discontinuity. This is known as the Gibb's effect. To change functions, click the "Change functions". You may also zoom the view by clicking anywhere on the plot. To return to the original scale, click the "Unzoom" button.