Chapter 12.3, Problem 1E

In Problems 1 and 2 solve the heat equation (1) subject to the given conditions. Assume a rod of length L.

1. $\begin{array}{l}u\left(0,t\right)=0,u\left(L,t\right)=0,t>0\\ u\left(x,0\right)=\{\begin{array}{l}1,0<x<L/2\\ 0,L/2<x<L\end{array}\end{array}$