Write the steady-state heat conduction equation (that is, the Laplace equation) for a Cartesian coordinate system for two spatial dimensions. During the winter (in which the air has an ambient temperature of \(-10^{\circ} \mathrm{C}\) ), a thin car window with dimensions \(1 \mathrm{~m}\) high by \(1.5 \mathrm{~m}\) wide is completely covered with ice. A poor quality electric heater is only able to apply heat to the bottom edge of the window at \(23^{\circ} \mathrm{C}\). The other edges of the window remain at the ambient temperature of the air. Determine if one can see through the middle third of the bottom half of the window if one waits for a long enough time by performing a numerical solution of the steady-state heat conduction equation with stated boundary conditions (that is, calculate the temperature at the mesh points \(u_{11}\) and \(u_{21}\) with a given mesh size of \(h=0.5 \mathrm{~m}\) ).