(New page: <math>f:\Omega \rightarrow \Re ^ m, \Omega \subset \Re ^n</math> <math>f</math> is said to be k-th continuously differentiable on <math>\Omega</math>, <math>f \in C^{k}</math>, if each ...) |
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<math>f:\Omega \rightarrow \Re ^ m, \Omega \subset \Re ^n</math> | <math>f:\Omega \rightarrow \Re ^ m, \Omega \subset \Re ^n</math> | ||
| − | <math>f</math> is said to be k-th continuously differentiable on <math>\Omega</math>, <math>f \in C^{k}</math>, | + | Function <math>f</math> is said to be k-th continuously differentiable on <math>\Omega</math>, <math>f \in C^{k}</math>, |
if each component of f has continuous partials of order k on <math>\Omega</math>. | if each component of f has continuous partials of order k on <math>\Omega</math>. | ||
Revision as of 13:22, 7 April 2008
$ f:\Omega \rightarrow \Re ^ m, \Omega \subset \Re ^n $
Function $ f $ is said to be k-th continuously differentiable on $ \Omega $, $ f \in 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
