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[tex]

\left | \frac{d \vec{f}}{d \vec{r}} \right | = \left | \frac{d(f_1,f_2)}{d(x,y)} \right | =

\frac{\partial f_1 \wedge \partial f_2}{\partial x \wedge \partial y}

=

\left |

\begin{bmatrix}

\frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y} \\

\frac{\partial f_2}{\partial x} & \frac{\partial f_2}{\partial y} \\

\end{bmatrix}

\right | = \frac{\partial f_1}{\partial x}\frac{\partial f_2}{\partial y} - \frac{\partial f_1}{\partial y} \frac{\partial f_2}{\partial x}

[/tex]

[tex]

\vec{\nabla} \cdot \vec{f} = \text{tr}\left ( \frac{d \vec{f}}{d \vec{r}} \right )

=

\text{tr}\left ( \begin{bmatrix}

\frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y} \\

\frac{\partial f_2}{\partial x} & \frac{\partial f_2}{\partial y} \\

\end{bmatrix} \right )

=

\frac{\partial f_1}{\partial x} + \frac{\partial f_2}{\partial y}

[/tex]

Realize how in the second equation I could to write the divergence in terms of df/dr. Now, what I want do is express the curl through of notation df/dr. Note that although of the first equation recall the expression of curl, is not the curl... Do you can help me with this?

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# Curl in terms of "fractional" notation

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