Consider the heat equation for b(t, x) on the unit interval, ∂b/∂t − ∂^2b/∂x^2 = 0, 0 < x < 1, t > 0. (a) [15 MARKS] Sol

[answerhappygod]

Consider the heat equation for b(t, x) on the unit
interval,
∂b/∂t − ∂^2b/∂x^2 = 0, 0 < x < 1, t > 0.
(a) [15 MARKS] Solve the initial-boundary value problem where the
initial conditions are
b(0, x) = 0,
and the boundary conditions are mixed and inhomogeneous,
∂b/∂x (t, 0) = 0, b(t, 1) = sin(ωt).
(b) [5 MARKS] Explicitly compute b(t, 0) in the limit that the
frequency of the boundary
condition ω → ∞