Basics of differential geometry
In school you learn about differentiation and integration during your senior years. This, however,
is restricted to twodimensional Euclidean space: a function f is given depending on a variable x
and can be differentiated or integrated with respect to this variable.
This principle can be generalized to dependence on several variables and  in a second step  to
more complicated geometries.
Membranes can be modelled as twodimensional objects; it is therefore possible to describe some of their features with the help of the Classical differential geometry of twodimensional surfaces.
