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\begin{document}
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\begin{center}
\textbf{Vector Calculus}

\textit{\textbf{Grad, Div and Curl}}
\end{center}

\textbf{Question}


Calculate $\textbf{\textrm{div}F}$ and $\textbf{\textrm{curl}F}$ for
the vector field

$\un{F} = f(z)\un{i} -f(z)\un{j}$


\textbf{Answer}

\begin{eqnarray*}
\textrm{div}\un{F} & = & \frac{\partial}{\partial x}
f(z)+\frac{\partial}{\partial y}
(-f(z))\\
\textrm{curl}\un{F} & = & \left | \begin{array}{ccc} \un{i} & \un{j} &
\un{k}\\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} &
\frac{\partial}{\partial z}\\
f(z) & -f(z) & 0
\end{array}
\right |
= f'(z)(\un{i}+\un{j})
\end{eqnarray*}

\end{document}