So i've hit my first course in PDEs, and we've been employing Fourier series in our solutions, but never learned about the series in particular. We've just been applying the formulae. I'm a little concerned that I may be off mark in how I applied the Fourier series to evaluate the constant in an infinite sum.

I've got a bit of a long question here that I 'think' i've solved, but I was hoping that one of you fine folks could take a read over my work and let me know if i'm on the right track?

Very much appreciated, thanks!

(PDF is too large, I've uploaded to google docs for viewing. Thanks!)

https://docs.google.com/viewer?a=v&p...MGVjMTA5&hl=en