(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 14:22, 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

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