$ f:\Omega \rightarrow \Re ^ m, \Omega \subset \Re ^n $

Function $ f $ is said to be k-th continuously differentiable on $ \Omega $, $ f \in \mathbb{C}^{k} $,

if each component of f has continuous partials of order k on $ \Omega $.

Example.

- For k=0, f is said to be coutinuous
- For k=1, f is said to be continuously differentiable