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Solve the heat equation ut = k uxx, 0 < x < L, t > 0...

Solve the heat equation ut = k uxx, 0 < x < L, t > 0

u(0, t) = u(L, t) = 0, t > 0

u(x, 0) = f(x), 0 < x < L

a) f(x) = 6 sin 9πx L

b) f(x) = 1 if 0 < x ≤ L/2 2 if L/2 < x < L

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