1. Limited time only! Sign up for a free 30min personal 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!

Divergence Operator Binding?

  1. Mar 26, 2012 #1
    I'm reading about the transport theorem in my vector calculus book. They state the following at the beginning of the section:

    Let F be a vector field on R^3. Let c(x, t) denote a flow line on F starting at location x and continuing out for t seconds. Let J(x, t) denote the Jacobian of c with respect to x, and with t fixed. We then have

    dJ/dt = [div F(c(x, t))] * J


    Now, what confuses me is the [div F(c(x, t))] part. Does that mean the divergence of F evaluated at c, or does it mean the divergence of of the composite function (F o c)? In other words, how tightly does the divergence operator bind to its operand?

    Expanding out dJ/dt piece by piece tells me that the statement in question should read "the divergence of F evaluated at c." I am pretty sure I did the expansion correctly, but I would still be curious to hear someone else chime in.

    P.S. Apologies for not TeXing any of this post. I only know Plain TeX, but my understanding is that the forums here only accept LaTeX.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted