Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is a smooth function?

  1. Dec 2, 2009 #1
    What is a "smooth" function?

    If someone tells you to consider a "smooth" function on the complex plane, what does that mean, exactly? Does it mean that the partial derivatives of the real and imaginary parts exist and are continuous? Does it mean something else?
     
  2. jcsd
  3. Dec 2, 2009 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: What is a "smooth" function?

    Usually, "let f be a smooth function" is an expression people use to be "let f be a function satisfying certain regularity conditions".

    Ex: for a smooth enough map f:R^2-->R, we have equality of the mixed partial derivative. Here, smooth means C^2.

    Sometimes also, people equate smooth with C^{infinity}.

    I've never seen smooth to mean holomorphic though...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What is a smooth function?
Loading...