Solve Laplace's equation
$\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} = 0$,
for $\phi(x, y)$ on a rectangular region given by $0 \le x \le a$ and $0 \le y \le b$. The boundary conditions are:
$\frac{\partial \phi}{\partial x} = 0$ on $x = 0, a$
$\frac{\partial \phi}{\partial y} = 0$ on $y = 0$
$\phi(x, b) = \cos\frac{\pi x}{a}$
Notice that these are derivative boundary conditions except at $y = b$. See if you can make a contour plot for
$a = 3$, $b = 2$ showing lines of constant $\phi$, and verify that the derivative boundary condition is satisfied.
