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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> | ||
| − | Function <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 \mathbb{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>. | ||
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* For k=0, f is said to be coutinuous | * For k=0, f is said to be coutinuous | ||
* For k=1, f is said to be continuously differentiable | * For k=1, f is said to be continuously differentiable | ||
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| + | [[Category:ECE662]] | ||
Latest revision as of 07:49, 10 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 \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
