In your answers below, for the variable λ type the word lambda, for γ type the word gamma; otherwise treat these as you would any other variable.

We will solve the heat equation

ut=4uxx,0
with boundary/initial conditions:

u(0,t)u(8,t)=0,=0,andu(x,0)={0,2,0
This models temperature in a thin rod of length L=8L=8 with thermal diffusivity α=4α=4 where the temperature at the ends is fixed at 00 and the initial temperature distribution is u(x,0)u(x,0).
For extra practice we will solve this problem from scratch.