MMAE 501: Engineering Analysis I Extra credit take-home Exam 1. In this question, we are looking to solve the Laplace equation 02q , 0-q Or2 dy2 = 0 on a semi-infinite strip, as shown below. y q(0,y) = 0 q(a,y) = 0 q(x,0) = f(x) a X The boundary conditions are q(0, y) = q(a, y) =0, for 0 + zy, find a transformation w = g() that maps this semi-infinite strip to the upper half plane. (c) Using part (b), now express the solution using the Cauchy integral formula for the upper half plane. (d) Evaluate your solutions in parts (a) and (c) for the case where the lower boundary condition is given by f(x) = 1 (your solutions for these previous parts should be for a general f(x)). Can you determine if they are the same