1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Continuity of the derivative Df

  1. Jan 6, 2008 #1

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    1. The problem statement, all variables and given/known data
    I'm reading this at the moment: "Let f:R^n-->R^n be of class C^1 (that is, assume Df exists and is continuous)"

    What does it mean?? If it means that for all x in R^n, the linear map Df(x):R^n-->R^n is continuous, then it's a triviality since all linear maps from R^n to R^m are continuous. So I am skeptical that this is what it means!

    What other option is there? That map that send x in R^n to the point Df(x) in the space of linear map is a continuous map? I highly doubt that!

    So what does it mean??
     
  2. jcsd
  3. Jan 6, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    C^1 usually means continuous partials.
     
  4. Jan 6, 2008 #3

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Thanks for the tip!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Continuity of the derivative Df
  1. Continuous derivative (Replies: 3)

Loading...