deletions | additions       diff --git a/Theory.tex b/Theory.tex  index f4c87d4..caec486 100644  --- a/Theory.tex  +++ b/Theory.tex 
...
$\vec{V}_{gr}=\frac{\mathrm\partial\omega}{\mathrm \partial\vec{k}}$   and the phase velocity is given by   $\V_{ph}=\frac{\omega}{k}$ $V_{ph}=\frac{\omega}{k}$