deletions | additions       diff --git a/Problem 1.tex b/Problem 1.tex  index cac7dec..1729976 100644  --- a/Problem 1.tex  +++ b/Problem 1.tex 
...
Define the function we will be using for the forward differencing as \[u=ge^{ikx_j}\] and the forward differencing equation as \[\Delta_x^{'}f_j=\frac{f_{j+1}-f_j}{\Delta}\] where are function $f$ will be our functuon $u$.\\  Putting this is we get \[\Delta_x^{'}u=\frac{ge^{ikx_{j+1}}-ge^{ikx_j}}{\Delta}\] define $x_{j+1}=x_j+\Delta$ then the above equation becomes \[\Delta_x^{'}u=\frac{ge^{ikx_j+\Delta}-ge^{ikx_j}}{\Delta}\]\\  Factoring we get \[\Delta_x^{'}u=\frac{ge^{ikx_j}(e^{ik\Delta}-1)}{\Delta}\] and taylor expanding we get  \[\approx=\frac{ge^{ikx_j}(1+ik\Delta+frac{(ik\Delta)^2}{2}}{\Delta}\] \[\approx\frac{ge^{ikx_j}(1+ik\Delta+frac{(ik\Delta)^2}{2}}{\Delta}\]