deletions | additions       diff --git a/We_can_define_the_Fourier__.tex b/We_can_define_the_Fourier__.tex  index a557c29..31762cf 100644  --- a/We_can_define_the_Fourier__.tex  +++ b/We_can_define_the_Fourier__.tex 
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\begin{equation}  z^3 + C = 2\pi\left((f_k-f)t + \frac{t^2}{2}\dot{f}_k + \frac{t^3}{6}\ddot{f}_k \right).  \end{equation}  If we use $z = At + B$, then $z^3 = A^3t^3 + 3A^2Bt^2 + 3AB^2t + B^3$.  Firstly, we can factor it into sine and cosine parts to give  \begin{align}