Problem $1$

For a vector $A=a_{x}3x^{2}cos(3y)-a_{y}sin(2x)y^2,$

a$)$ Write a MATLAB code to evaluate $o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}A*dl$ around the contour shown in figure

b$)$ Evaluate grad$$A then write a MATLAB code to evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(gradA)*ds$ over the shaded area

c$)$ Compare the results of the previous two points and comment.

Hints:

$o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}A*dl$ is translated into ${\displaystyle \underset{?}{\overset{?}{}}}A*dl$ when used in computer calculations

$-{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(gradA)*ds$ is translated into ${\displaystyle \underset{?}{\overset{?}{}}}({\displaystyle \underset{?}{\overset{?}{}}}(gradA)*dx)dy$ when used in computer calculations

The discretization strategy is to use $\{\begin{array}{c}<msup><mrow><mn>0</mn><mn>.</mn><mn>1</mn></mrow><mrow><mi>*</mi><mi>*</mi></mrow></msup>\end{array}($minimum dimension in the problem$)$