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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

$\un{F} = xy^2\un{i} -yz^2 \un{j} + zx^2\un{k}$


\textbf{Answer}

\begin{eqnarray*}
\textrm{div}\un{F} & = & \frac{\partial}{\partial x}(
xy^2 )+\frac{\partial}{\partial y}(
-yz^2 ) +\frac{\partial}{\partial z}(
zx^2 )\\
& = & y^2-z^2+x^2\\
\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}\\
xy^2 & -yz^2 & zx^2
\end{array}
\right |
=2yz \un{i} -2xz\un{j} -2xy\un{k}
\end{eqnarray*}

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