Double Integrals: Applications & Examples

Q.6 Use Dirichlet's integral to evaluate fff xyz dx dy dz throu... | Filo

SOLVED: Text: Provide all the details in the proof of the formula for the solution of the Dirichlet problem in a strip discussed in Section 1.3. Recall that it suffices to compute the solution at the points z = iy with 0 < y < 1. (a) Show that if then, This leads to two separate cases: either 0 < y ≤ 1/2 and θ = π/2, or 1/2 ≤ y < 1 and θ = -π/2. In either case, show that (b) In the integral make the change of variables t = F(e^iφ). Observe that and then ta