This problems solves Laplaces equation on a circle of radius 1 with the Boundary Element Method (BEM). The circle has 16 nodes and 16 elements around the circumference and the basis functions used are cubic Hermite. A Dirichlet boundary condition of x^2 + 2xy -y^2 is set and the normal derivative is solved for. The numerical results are compared to the known analytic formula for this problem.