Solve the heat equation u t = k 2u x2 subject to the following conditions: u(0, t)=0 u(L, t)=0 u(x, 0) = f(x). What happens as t ? [Hints: 1. It is known that if u(x, t) = (x) G(t), then 1 kG dG dt = 1 d2 dx2 . 2. Use formula sheet.]

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