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

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