Solve Laplace’s equation inside a semicircle of radius a(0 < r < a, 0 < θ <...

Solve Laplace’s equation inside a semicircle of radius a(0 < r < a, 0 < θ < π) subject to the boundary conditions [Hint: In polar coordinates,

*(a) u = 0 on the diameter and u(a, θ) = g(θ)

(b) the diameter is insulated and u(a, θ) = g(θ)