\chapter{Mathematical tools}
-\section{Vector space}
+\section{Vector algebra}
+
+\subsection{Vector space}
\label{math_app:vector_space}
\begin{definition}
The addition of two vectors is called vector addition.
\end{remark}
+\subsection{Dual space}
+
+\subsection{Inner and outer product}
+
+\begin{definition}
+The inner product ...
+\end{definition}
+
+\begin{definition}
+The outer product ...
+\end{definition}
+
\section{Spherical coordinates}
\section{Fourier integrals}