Task 1: Divergence and curl of a vector field
(a) For the given vector field
$\vec{A} = 3re^{-(\frac{r^2}{16})}\hat{r}$,
find $div(\vec{A})$ analytically and using MATLAB* (transformation to the Cartesian c.s. is
required). Plot the vector field $\vec{A}$ and the contours of the constant values of the
divergence in the same figure. Use two interval values: $[-1 \le x, y \le 1]$ and
$[-10 \le x, y \le 10]$ with 0.1 step in each axis to produce two plots. Compare the value of
the divergence at points $P_1 = (x_1, y_1) = (0.6, 0.6)$ and $P_2 = (x_2, y_2) = (5, 7)$. Create a
comparison table. Explain the discrepancy.
