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Question

Math 6410 • ODE

Fall 2016 • Question 7

The laplacian in polar coordinates is \begin{equation} \nabla ^2u=\frac {1}{r}\frac {\partial }{\partial r} \left (r\frac {\partial u}{\partial r}\right ) +\frac {1}{r^2}\frac {\partial ^2u}{\partial \theta ^2}. \tag {1} \end{equation}

Raw LaTeX

The laplacian in polar coordinates is
\begin{equation}
  \nabla^2u=\frac{1}{r}\frac{\partial}{\partial r}
  \left(r\frac{\partial u}{\partial r}\right)
  +\frac{1}{r^2}\frac{\partial^2u}{\partial\theta^2}.
  \tag{1}
\end{equation}