Exercise 102

In the region described by $0 < x < 1$ and $0 < y < 2$, solve the problem $$\Delta u = 0, \quad u(x,0) = 0.1 \sin (\pi x), \quad u(x,2) = 0, \quad u(0,y) = 0, \quad u(1,y) = 0 .$$