deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 3740bab..b3ae690 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\end{bmatrix} \]  This leaves us then with \[\tilde{A}(z)=\tilde{A}(0)\left( cos \beta_c z -\frac{i \delta}{\beta_c} sin \beta_c z \right) e^{i \delta z} \]  \[\tilde{B}(z)=\tilde{A}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} \]  Looking back at my slides I wrote that $\tilde{B}(z)=\tilde{B}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} $, which given my initial conditions would be wrong since $\tilde{B}(0)=0$. Thankfully, this error doesn't propagate through the rest of the presentation as that error only shows up on slide 8 and the rest of the figures I made are still accurate. I want to point out another error I made in the paper in regards to figure 1 here. The error is that in the figure in the paper, I wrote the same error for the power, corresponding to the blue line in figure one. I wrote $\frac{P_a(z)}{P_b(o)}$