MAP 4306 Study Guide - Quiz Guide: Heat Equation, Horse Length
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X2 + x, u(x, 0) = f (x), X (l, t) = 7. (a) calculate the total thermal energy in the one-dimensional rod (as a function of time). (100 points) (b) from part (a), determine the value of for which an equilibrium exists. For this value of , determine (10 bonus points) limt u(x, t). Hints: this is a homework exercise, so just copy your solution from the homework notebook. In case you didn"t do it, formulas (1. 2. 4) and (1. 2. 8) in the text can help. If you want to, you may assume c = = k0 = 1. Q so in our case k = 1, q/c = x. There is some leeway in what c, are, but to solve the problem we"ll assume they are constant. We have to nd the total energy in the rod as a function of time; in other words we have to nd e(x, t) dx.
