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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

$\un{F} = f(x)\un{i} + g(y)\un{j} + h(z)\un{k}$


\textbf{Answer}

\begin{eqnarray*}
\textrm{div}\un{F} & = & \frac{\partial}{\partial x}
f(x)+\frac{\partial}{\partial y}
g(y) +\frac{\partial}{\partial z}
h(z)\\
& = & f'(x) + g'(y) + h'(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(x) & g(y) & h(z)
\end{array}
\right |
= \un{0}
\end{eqnarray*}

\end{document}