4. (15 points) Consider the Heat Equation ut = aurr u(x, 0) = -1, 1, u(0, t) = u(27, t) =0, t20 (a) Give the Sine Series for u(x, 0). Include the first four nonzero terms. Each coefficient should be a single reduced fraction with no trig functions and no decimals. (b) Give the solution to the Heat Equation, u(r, t). Include the first four nonzero terms. Each coefficient should be a single reduced fraction with no trig functions and no decimals