Kreyszig's introduction of the normal derivative
$u_n = \partial u / \partial n$
leaves me a bit puzzled as to what variable $n$ is if $u$ is a function of $x$ and $y$.
The trailing example uses a condition for one of the boundaries specified as $u_n = 6x$ and the solution steps deduces $\dfrac {\partial u_{ij}} {\partial n} = \dfrac {\partial u_{ij}} {\partial y} = 6x$ out of thin air.
So what exactly is the normal derivative? Is it simply an interpretation of a normal vector standing up from $u$ if it's treated as a surface, i.e. $\dfrac {\partial u_{ij}} {\partial n} = \dfrac {\partial u_{ij}} {\partial x} + \dfrac {\partial u_{ij}} {\partial y}$ ?