PDE Homework #3: Separation of Variables for the Heat Equation Use separation of variables to solve the following heat equation problem with inhomogeneous boundary conditions: 2 2 3 (0 ) 20 (40 ) 100 ( 0) 40 u u t x u t u t u x x ? ? ? ? ??? ? ? After you have found the infinite series solution using separation of variables then use Matlab to evaluate your series solution in order to plot the temperature profile at a few fixed values of time. In other words plot u(xt) versus x for a few fixed values of t. Put all the temperature curves on a single plot and label the t value for each curve.

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