Jean Baptiste Fourier published a paper in 1807 on his theory of heat flow, in which he postulated that any function defined in a region of space (or time) could be "decomposed" as a sum of sin waves. This forms the basis of a tremendous amount of physics, with applications in practically every field (including equalizers - in the figure, you can see that itunes thinks we want to enhance the base and treble for classical music, in this case a spectacular rendition of one of my favorite pieces of Beethoven )
The continuous version of Fourier's series, the Fourier Transform (spoofed here in xkcd) will be covered a bit later in the term. (I am not sure why the cat has such pronounced periodicities...)
I welcome your comments on the class and this website.
Send them to steven.pollock at colorado.edu