Readme first! I am still in the process of revising these notes, and I have posted my first version, and the vastly updated revision.
Alrighty, in this epic tome I introduced the Fourier series. I reviewed the Gibbs phenomena, when we have discontinuities the partial sums appear to sort of “overshoot” the function near the discontinuities; the Fourier series converges everywhere else except at the discontinuous points if there are countably many discontinuities and if the function is 
At any rate, I didn’t get to any real application unfortunately. That will be next time! I did refer to two free sets of lecture notes available on the math.ucdavis.edu site; one is the “Advanced Linear Algebra” lecture notes (the math 67 text), the other is the graduate level analysis book (which is freely available online).
Download (fourth(?) version) my lecture notes. As always, comments welcome! (Addendum I’ve just finished a great deal of notes on Fourier transforms and Fourier series, so I’ve made the notes “beta version” but still under construction!)
Next time I think I will give a few examples of using the Fourier series and transform to solve various differential equations, or just jump ahead to the Spherical Harmonics and Legendre Polynomials…the professor really is racing along quite well. Addendum (3 January 2009) I’ve covered a number of things, and I think that I will try to get to spherical harmonics next, but I am also typing up my notes on abstract algebra. I think that my notes on abstract algebra are rather straightforward and really quite keen, but I don’t know whether it’ll be coherent enough. I’ve got plenty of examples, and loosely follow Serge Lang’s book Algebra. When I am done with group theory, I’ll upload those notes.
