# One Dimensional Heat Equation on a Finite Rod

Can someone please solve this heat equations with details on how to arrive at the solution.?

Solve the heat equation:

u_t = 3*u_xx

with the following I.C/B.C:

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

u(x,0)=L*[1-cos(2*Pi*x/L)]

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#### Solution Summary

The solution shows how to apply separation of variables to solve the heat equation on a finite rod.

The process demonstrates how to use Fourier expansion to obtain a solution that satisfies the initial and boundary conditions.

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