Math 314 Lecture 06: Monday, September 20th 1999.
On Friday's lecture, it was mentioned that the number of dimensions in the
function space is uncountably infinite, wheras the number of functions in
the orthonormal set is countably infinite. Today, I started with a brief
diversion explaining this difference using the technique of Cantor
Diagonalization.
Then we explored the standard Fourier Series, which is periodic
on (-Pi,Pi). A couple of examples were worked out. These Fourier
Series were then plotted in Maple, in order
to see how well they converge to the original functions.
Some exercises were assigned which are due on Wednesday, along with the
exercises assigned on Friday.
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Revised 20 September 1999 by
John Hebron.