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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

$\un{F} = y\un{i} + x\un{j}$


\textbf{Answer}

\begin{eqnarray*}
\textrm{div}\un{F} & = & \frac{\partial}{\partial x}(
 y)+\frac{\partial}{\partial y}(
 x) +\frac{\partial}{\partial z}(
 0) = 0+0=0\\
\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}\\
y & x & 0
\end{array}
\right |
=(1-1)\un{k}=0
\end{eqnarray*}


\end{document}