diff options
| -rw-r--r-- | buch/papers/kugel/applications.tex | 1 | ||||
| -rw-r--r-- | buch/papers/kugel/spherical-harmonics.tex | 29 |
2 files changed, 14 insertions, 16 deletions
diff --git a/buch/papers/kugel/applications.tex b/buch/papers/kugel/applications.tex index 10bf153..481a3a5 100644 --- a/buch/papers/kugel/applications.tex +++ b/buch/papers/kugel/applications.tex @@ -18,6 +18,7 @@ the most interesting applications we came across during our research. \subfigure[Gauss' Law \label{kugel:fig:eeg-flux}]% {\includegraphics[width=.4\linewidth]{papers/kugel/figures/flux}} \caption{ + Electroencephalography. \label{kugel:fig:eeg} } \end{figure} diff --git a/buch/papers/kugel/spherical-harmonics.tex b/buch/papers/kugel/spherical-harmonics.tex index b46d64d..b540531 100644 --- a/buch/papers/kugel/spherical-harmonics.tex +++ b/buch/papers/kugel/spherical-harmonics.tex @@ -33,16 +33,6 @@ that mathematics offers us. \subsection{Eigenvalue Problem} \label{kugel:sec:construction:eigenvalue} -\begin{figure} - \centering - \includegraphics{papers/kugel/figures/tikz/spherical-coordinates} - \caption{ - Spherical coordinate system. Space is described with the free variables $r - \in \mathbb{R}_0^+$, $\vartheta \in [0; \pi]$ and $\varphi \in [0; 2\pi)$. - \label{kugel:fig:spherical-coordinates} - } -\end{figure} - From Section \ref{buch:pde:section:kugel}, we know that the spherical Laplacian in the spherical coordinate system (shown in Figure \ref{kugel:fig:spherical-coordinates}) is is defined as @@ -190,13 +180,20 @@ require a dedicated section of its own. \begin{figure} \centering - \includegraphics[ - scale = 1.2, - trim = 0 40 0 0, clip, - ]{papers/kugel/figures/tikz/legendre-substitution} + \subfigure[Spherical coordinates. \label{kugel:fig:spherical-coordinates}] + {\includegraphics[width=.45\linewidth]{papers/kugel/figures/tikz/spherical-coordinates}} + \qquad + \subfigure[Substitution. \label{kugel:fig:legendre-substitution}] + {\includegraphics[ + width=.45\linewidth + % scale = 1.2, + % trim = 0 40 0 0, clip, + ]{papers/kugel/figures/tikz/legendre-substitution}} \caption{ - Sketch of the geometry. - \label{kugel:fig:legendre-substitution} + (a) Spherical coordinate system. Space is described with the free variables + $r \in \mathbb{R}_0^+$, $\vartheta \in [0; \pi]$ and $\varphi \in [0; + 2\pi)$. (b) Geometrical intuition for the substitution to obtain the + Legendre equation. } \end{figure} |