this is for holding javascript data
Terris Becker edited untitled.tex
almost 8 years ago
Commit id: 0a1cd4cba1679c29b02c5d298558d84bd3e81048
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index cb8952f..903c128 100644
--- a/untitled.tex
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(ln|f(x,y)|)_{yy}&= (\frac{uu_y+vv_y}{u^{2}+v^{2}})_y\\
&= \frac{(uu_y + uu_{yy} +v_yv_y + vv_{yy})(u^{2}+v^{2})-(uu_y + vv_y)(2uu_y+2vv_y)}{(u^{2}+v^{2})^{2}}
\end{align*}
Now consider the Laplace equation,
\begin{align*}
(ln|f(x,y)|)_{xx}+(ln|f(x,y)|)_{yy}
&=\frac{(uu_x + uu_{xx} +v_xv_x + vv_{xx})(u^{2}+v^{2})-(uu_x + vv_x)(2uu_x+2vv_x) + (uu_y + uu_{yy} +v_yv_y + vv_{yy})(u^{2}+v^{2})-(uu_y + vv_y)(2uu_y+2vv_y)}{(u^{2}+v^{2})^{2}}
\end{align*}
\end{proof}