Basics of differential geometry

In school you learn about differentiation and integration during your senior years. This, however, is restricted to two-dimensional 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 two-dimensional objects; it is therefore possible to describe some of their features with the help of the Classical differential geometry of two-dimensional surfaces.