\part{Residue theory}


\begin{definition}[Pole]
\end{definition}

\begin{definition}[Residue]
\end{definition}

\begin{definition}[Laurent series]
\end{definition}

\begin{definition}[Meomorphic function]
\end{definition}



\begin{theorem}[Residue theorem]
\end{theorem}



\begin{theorem}[Picard's little theorem]
\end{theorem}
\begin{theorem}[Picard's great theorem]
\end{theorem}

\section{Application to real analysis}

Beyond the theory of residues being an interesting part of mathematics, it also finds use in the evaluation of integrals of real functions, some of which are highly nonelementary or even impossible to calculate otherwise!

- Euler function 
\[ \varphi(q) = \prod^{\infty}_{k=1} (1-q^k), |q| < 1\]