deletions | additions       diff --git a/section_Reflection_Coefficients_The_reflection__.tex b/section_Reflection_Coefficients_The_reflection__.tex  index 02f17c7..ee4d32b 100644  --- a/section_Reflection_Coefficients_The_reflection__.tex  +++ b/section_Reflection_Coefficients_The_reflection__.tex 
...
\mathbf{H}_{0\mathrm{i}} e^{-2 \pi i \left( \mathbf{w}'_{\mathrm{i}} \cdot \mathbf{r} - i \mathbf{w}''_{\mathrm{i}} \cdot \mathbf{r} \right)} \times \mathbf{\hat{n}} + \mathbf{H}_{0\mathrm{r}} e^{-2 \pi i \left( \mathbf{w}'_{\mathrm{r}} \cdot \mathbf{r} - i \mathbf{w}''_{\mathrm{r}} \cdot \mathbf{r} \right)} \times \mathbf{\hat{n}} = \mathbf{H}_{0\mathrm{t}} e^{-2 \pi i \left( \mathbf{w}'_{\mathrm{t}} \cdot \mathbf{r} - i \mathbf{w}''_{\mathrm{t}} \cdot \mathbf{r} \right)} \times \mathbf{\hat{n}}  \end{equation}  %  With the coordinate origin on the boundary, at the point $\mathbf{r}=0$, Eqs.\ \ref{eq:eboundary} and \ref{eq:hboundary}  become %  \begin{equation}  \left(\mathbf{E}_{0\mathrm{i}} + \mathbf{E}_{0\mathrm{r}} \right) \times \mathbf{\hat{n}} = \mathbf{E}_{0\mathrm{t}} \times \mathbf{\hat{n}} 
...
%  \begin{equation}  \left( \mathbf{H}_{0\mathrm{i}} + \mathbf{H}_{0\mathrm{r}} \right) \times \mathbf{\hat{n}} = \mathbf{H}_{0\mathrm{t}} \times \mathbf{\hat{n}}  \end{equation}  %  These equations can then be broken into parallel and perpendicular components.  %  \begin{equation}  \left[ \left( E_{\parallel\mathrm{i}} + E_{\parallel\mathrm{r}} \right) \mathbf{\hat{e}}_{\parallel} + \left( E_{\perp\mathrm{i}} + E_{\perp\mathrm{r}} \right) \mathbf{\hat{e}}_{\perp}\right] \times \mathbf{\hat{n}} = \left[ E_{\parallel\mathrm{t}} \mathbf{\hat{e}}_{\parallel} + E_{\perp\mathrm{t}} \mathbf{\hat{e}}_{\perp} \right] \times \mathbf{\hat{n}}  \end{equation}