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

Homework Help: Understanding Differential Notation

  1. Dec 20, 2005 #1
    The four velocity component [tex]u^\mu[/tex] with coordinate of [tex]x^\mu(\lambda)[/tex] is given by

    [tex]u^\mu = \frac{dx^\mu}{d\lambda}[/tex]

    where [tex]\lambda[/tex] is the proper time. So, the component of acceleration [tex]a^\mu[/tex] is

    [tex]a^\mu = \frac{du^\mu}{d\lambda}[/tex]

    Using the chain rule we have

    [tex]a^\mu = \frac{\partial u^\mu}{\partial x^\alpha} \frac{dx^\alpha}{d\lambda} = u^\alpha \partial_{\alpha}u^\mu[/tex]

    Everything was straight forward except the last part, I don't understand what the notation of [tex]\partial_{\alpha}[/tex] meant.
    Last edited: Dec 20, 2005
  2. jcsd
  3. Dec 20, 2005 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [itex]\partial_{\alpha}[/itex] is the covariant 4-gradient. It means nothing other than the following:

    [tex]\partial_{\alpha}=\frac{\partial}{\partial x^{\alpha}}[/tex]
    Last edited: Dec 20, 2005
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook