1D transient heat conduction equation (PDE) is given by at 0 x L x pc where t is temperature, 0 is time. Boundary conditions are Initial condition is at k ktx(0,0) = h[too t(0, 0)] ktx(L,0) = h[t(L,0) to] t(x,0) = t(0)(x) (a) Define a new variable to replace original temperature variable t to make the problem homogeneous and write down the new PDE and BCs (b) Find the eigencondition and eigenfunctions for the new homogeneous problem.