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\title{General Mathematics and CPS II}
\author{Exercise 20}
\date{April 25, 2014}
\maketitle

\begin{enumerate}

\item Recall the definition of the Fourier series,
\[
  v(x) = \sum_{k=-\infty}^\infty \hat v_k \, \e^{\i k x} \,.
\]
Show that
\[
  \hat v_k = \frac1{2\pi} \int_0^{2\pi} \e^{-\i kx} \, v(x) \, \d x \,.
\]
(You may assume you can freely exchange summation and integration, and
that all sums converge.)

\item Handout, Exercise 1.

\item Handout, Exercise 2.

\end{enumerate}
\end{document}
