Consider a $4-$node quadrilateral with nodes at $(0,0),(5,0),(6,3),$ and $(0,6).$ Find

the contribution of a uniform source $($f$=1)$ to each of the nodes. Use mapping and

Gauss Quadrature. Answers: $6\mathrm{.}75,5\mathrm{.}5,6,7\mathrm{.}25.$ Note: this will require you to compute the Jacobian matrix and determinant that will be a function of the parent coordinates.

You can use a $2$ x $2$ Gauss rule to evaluate your mapped integrals.

$2.$ For the element above, the values for u at each of the four nodes listed

sequentially above are $1\mathrm{.}6,2\mathrm{.}2,3\mathrm{.}1,$ and $4\mathrm{.}0.$ Find the values of x$,$ y$,$ u$,$ and the

gradient of u at the centroid $(\backslash$xi $=0,\backslash$eta $=0).$ Answers for the gradient: $0\mathrm{.}0706,0\mathrm{.}3587.$

Note that this will require computation of $[$J$],$ J$,$ and $[$J$]-1.$