A related point of entry is the "Gibbs Phenomenon" -- http://en.wikipedia.org/wiki/Gibbs_phenomenon http://en.wikipedia.org/wiki/Gibbs_phenomenon . If I rememb

A related point of entry is the "Gibbs Phenomenon" -- http://en.wikipedia.org/wiki/Gibbs_phenomenon http://en.wikipedia.org/wiki/Gibbs_phenomenon . If I remember my "history of the Fourier transform" correctly, before the difference between the sup-norm and L2 norms were fully understood by everyone (e.g., by the late 1800s), the sense of convergence of a Fourier series to a square wave was confusing. In what sense did the Fourier series represent the square wave? When was it a good model and when would it fail?