I've just written the final exam in my introductory course to functional analysis (2nd year bachelor degree). I felt quite well prepared but nevertheless found the exam pretty challenging in the timeframe of two hours. I'd appreciate any comments about what you think about it! The exam can be found here: http://www.math.lmu.de/~michel/SS12_FA_Final_Test_01.pdf
In particular I'd appreciate any hints how to solve 6 ii), which states:
Use the fourier-series of $f(x)=\begin{cases}x^2 &\mbox{ for } x\in[0,\pi] \\ (2\pi-x)^2 &\mbox{ for } x\in (\pi,2\pi ]\end{cases} $ to calculate $\sum_{n\in\mathbb{N}}\frac{(-1)^{n-1}}{n^2}$