this is for holding javascript data
Benedict Irwin edited Summary.tex
over 9 years ago
Commit id: ccd0f5154338d1fa41e1a659a028b4e3b56f3289
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index 8ede3a7..aa4adc2 100644
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...
\section{Summary of Operators}
\begin{equation}
\nabla = \begin{bmatrix}
\partial_x^2\partial_y\partial_z \partial_x \\
\partial_x\partial_y^2\partial_z \partial_y \\
\partial_x\partial_y\partial_z^2 \partial_z \end{bmatrix}\\ \\
\nabla\cdot =
\begin{bmatrix}
\partial_z^{-1}\partial_y^{-1} \partial_x &
\partial_z^{-1}\partial_x^{-1} \partial_y &
\partial_y^{-1}\partial_x^{-1} \partial_z \end{bmatrix} \\ \\
\nabla \times =
\begin{bmatrix}
...
\nabla^4_{scalar} = (\partial_x^2 + \partial_y^2 + \partial_z^2)^2 \\\\
\nabla^T\nabla=\partial_x^2\partial_y^2\partial_z^2( \nabla^T\nabla= \nabla\cdot\nabla = \partial_x^2 + \partial_y^2 + \partial_z^2
) \\\\
\frac{\nabla^T\nabla}{\nabla\cdot\nabla} = \partial_x^2\partial_y^2\partial_z^2 \\\\
\nabla\cdot(\nabla(\nabla\cdot)) =
\begin{bmatrix}
\partial_x^2\partial_y^{-1}\partial_z^{-1} + \partial_y\partial_z^{-1} + \partial_y^{-1}\partial_z \\
\partial_y^2\partial_x^{-1}\partial_z^{-1} + \partial_x\partial_z^{-1} + \partial_x^{-1}\partial_z \\
\partial_z^2\partial_x^{-1}\partial_y^{-1} + \partial_x\partial_y^{-1} + \partial_x^{-1}\partial_y ...
\end{bmatrix}^T \\\\
\nabla \times (\nabla \times (\nabla \times))=