Derive the method of weighted residuals (mwr) weak form and the principle of virtual work (pvw) weak form of the problem statement. define the functional g(u, u ) % and clearly specify the function spaces for u(x) and u (x) , and the type of boundary conditions in each case. b) for the pvw weak form, if we restrict the space of functions for u(x) and u (x) to polynomials i. e. 0 1 2 0 1 2 0 1 2 0 1 2 ( ) ˆ( ) ( ) ˆ ( ) n n n n u x u x a x a x a x a x u x u x a x a x a x a x             l l comment if this approximation belongs to the function spaces in