Next: The PDE. Up: A Look at Previous: The domain and

The Laplace equation.

The final basic PDE we will consider governs steady heat conduction in a plate of length $\ell$ and height h such as shown in figure 12. In this example, one half of the boundary of the plate is being kept at 100 degrees Centigrade and the other half at zero.

**Figure 12:** Heat conduction in a plate.
$\begin{figure} \begin{center} \leavevmode \epsffile{figures/lapplate.ps} \end{center}\end{figure}$

The PDE.
The boundary conditions.
Smoothness of the solution.
About properly posed problems.
Improperly posed problems that do have solutions.
About the numerical solution.

Next: The PDE. Up: A Look at Previous: The domain and