Section 1
The Heat Equation and Initial and Boundary Conditions
Formulate a boundary value problem modeling heat conduction in a thin bar of length $L$, if the left end is kept at temperature zero and the right end is insulated. The initial temperature in the cross section at $x$ is $f(x)$.
Formulate a boundary value problem modeling heat conduction in a thin bar of length $L$, if the left end is kept at temperature $\alpha(t)$ and the right end at temperature $\beta(t)$. The initial temperature in the cross section at $x$ is $f(x)$.
Formulate a boundary value for the temperature function in a thin bar of length $L$ if the left end is kept insulated and the right end at temperature $\beta(t)$. The initial temperature in the cross section at $x$ is $f(x)$.