T3 finite element is defined over triangle ABC (in physical coordinates). The vertices of this triangle have
the following coordinates: A(5,-7),B(-3,8), and C(-6,-5).
Problem 1.
Calculate the partial derivatives of T3 basis functions with respect to the physical coordinates x
and y.
Problem 2.
a\int_(\Delta ABC) f(x,y)dS
where f(x,y)=5x^(2)-3y^(2)+6x-y.
bf(x,y)=cos(\pi x)-sin(y) is going to be represented by T3 basis functions over
triangle ABC. Calculate the values of the degrees of freedom C_(i) in the linear combination that
represents f(x,y) at the vertices of the triangle ABC :
f(x,y)=\sum_(i=1)^m C_(i)N_(i)(x,y)
Note: please use radians when evaluate the trigonometric functions.