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!

About Nabla and index notation

  1. Oct 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Can I, for all purposes, say that Nabla, on index notation, is $$\partial_i e_i$$ and treat it like a vector when calculating curl, divergence or gradient?
    For example, saying that $$\nabla \times \vec{V} = \partial_i \hat{e}_i \times V_j \hat{e}_j = \partial_i V_j (\hat{e}_i \times \hat{e}_j) = \partial_i V_j \epsilon_{ijk} \hat{e}_k$$
    I have a feeling that is wrong, I've found all kinds of variations of this notation on the internet, almost no one seems to use the unit vectors, and that confuses me, being a total beginner on this kind of notation.

    2. Relevant equations
    ----

    3. The attempt at a solution
    ------

     
  2. jcsd
  3. Oct 23, 2016 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It's an 'abuse of notation', but it can be useful as a mnemonic. If it helps you remember the formulas, that's fine. But try not to lose sight of the fact that it is not strictly correct. For instance ##\nabla f## is not strictly a vector (it's a covector, aka one-form or dual vector). You probably don't need to understand nuances like that yet if you're just starting but it's good to remember that the notation is just a mnemonic, to avoid confusion later on.
     
  4. Oct 23, 2016 #3
    Yes i have very clear what do gradients or divergences do....in a practical way (direction of max change, and flux per EDIT:volume unit :) i believe?) but I'm still struggling setting up the bridge between my vector calculus knowledge, physics knowledge, and this notation.... But the course is only starting, and I'm trying to prove vector identities.

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: About Nabla and index notation
  1. Index Notation (Replies: 9)

  2. Tensor index notation (Replies: 4)

Loading...