Assignment:
Q1. Consider the Dirichlet Problem where the temperature within a rectangular plate R is steady-state and does not change with respect to time. Find the temperature u(x,y) within the plate for the boundary conditions below and where f(x) =3x.
Q2. Solve the Dirichlet problem for steady-state (constant with respect to time) temperature within the wedge shown below. Find the temperature u (ρ, Φ)within the wedge. The temperature along the arc is u(Φ) = Φ.
Hint: For the solution in r, which is the radius, the coefficient for one of the two independent solutions must be zero, since the solution must be finite (can't go to infinity) when ρ=0.
Provide complete and step by step solution for the question and show calculations and use formulas.