Consider
subject to u(0, t) = 0, u(L, t) = 0, and u(x, 0) = f(x).
*(a) What is the total heat energy in the rod as a function of time?
(b) What is the flow of heat energy out of the rod at x = 0? at x = L?
*(c) What relationship should exist between parts (a) and (b)?
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