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\begin{document}
\begin{center}
\emph{TOPICS}
\end{center}
\bigskip
\begin{itemize}
\item First order equations
\begin{itemize}
\item linear equations
\item conservation laws, shocks, entropy
\item geometrical optics
\end{itemize}
\item one dimensional wave equation
\begin{itemize}
\item D'Alembert
\item energy methods
\item characteristics
\end{itemize}
\item one dimensional heat equation
\begin{itemize}
\item explicit formula
\item energy methods
\item maximum principle
\end{itemize}
\item Duhamel principle
\item Wellposednness
\item half space - even/odd functions
\item polar coordinates
\item Laplace/Poisson/Helmholtz equation
\begin{itemize}
\item mean value
\item Rayleigh quoatient
\item Dirichlet principle
\end{itemize}
\item Sturm Liouville
\begin{itemize}
\item convergence
\item eigenvalues, eigenfunctions
\end{itemize}
\item Separation of Values
\begin{itemize}
\item 1d,2d and 3d
\item inhomogenous problem
\item Bessel equation
\item polar coordinates
\end{itemize}
\item Green's function
\item distributions - delta function
\item finite elements
\end{itemize}
\end{document}