Calculate the divergence of each of the following vector fields. You may look
up the formulas for divergence in curvilinear coordinates.
-
\begin{equation}
\hat{F}=z^2\,\hat{x} + x^2 \,\hat{y} -y^2 \,\hat{z}
\end{equation}
-
\begin{equation}
\hat{G} = e^{-x} \,\hat{x} + e^{-y} \,\hat{y} +e^{-z} \,\hat{z}
\end{equation}
-
\begin{equation}
\hat{H} = yz\,\hat{x} + zx\,\hat{y} + xy\,\hat{z}
\end{equation}
-
\begin{equation}
\hat{I} = x^2\,\hat{x} + z^2\,\hat{y} + y^2\,\hat{z}
\end{equation}
-
\begin{equation}
\hat{J} = xy\,\hat{x} + xz\,\hat{y} + yz\,\hat{z}
\end{equation}
-
\begin{equation}
\hat{K} = s^2\,\hat{s}
\end{equation}
-
\begin{equation}
\hat{L} = r^3\,\hat{\phi}
\end{equation}