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\section{Summary of Operators}  \begin{equation}  \nabla = \begin{bmatrix} \partial_x^2\partial_y\partial_z \\ \partial_x\partial_y^2\partial_z \\ \partial_x\partial_y\partial_z^2 \end{bmatrix}\\ \\  \nabla\cdot =  \begin{bmatrix} \partial_z^{-1}\partial_y^{-1} & \partial_z^{-1}\partial_x^{-1} & \partial_y^{-1}\partial_x^{-1} \end{bmatrix} \\ \\  \nabla \times =  \begin{bmatrix}  0 & -\partial_z & \partial_y \\  \partial_z & 0 & -\partial_x \\  -\partial_y & \partial_x & 0  \end{bmatrix} \\ \\  \nabla(\nabla \cdot)=  \begin{bmatrix}  \partial_x^2 & \partial_y\partial_x & \partial_z\partial_x \\  \partial_x\partial_y & \partial_y^2 & \partial_z\partial_y \\  \partial_x\partial_z & \partial_y\partial_z & \partial_z^2  \end{bmatrix} \\ \\  \nabla^2=  \begin{bmatrix}  \partial_x^2 + \partial_y^2 + \partial_z^2 & 0 & 0 \\  0 & \partial_x^2 + \partial_y^2 + \partial_z^2 & 0 \\  0 & 0 & \partial_x^2 + \partial_y^2 + \partial_z^2  \end{bmatrix} \\ \\  \nabla \times (\nabla \times)=  \begin{bmatrix}  -\partial_z^2-\partial_y^2 & \partial_y\partial_x & \partial_z\partial_x \\  \partial_x\partial_y & -\partial_z^2-\partial_x^2 & \partial_z\partial_y \\  \partial_x\partial_z & \partial_y\partial_z & -\partial_y^2-\partial_x^2   \end{bmatrix} \\ \\  \end{equation}