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Intuition for Covariant derivative of a Tensor Field

  1. May 13, 2008 #1
    Hi. I am attempting to gain some intuition for what the covariant derivative of a tensor field is.

    I have a good intuition about the covariant derivative of vector fields (measuring how the vector changes as you move in a particular direction), and I understand how to extend the covariant derivative to tensors with the leibnitz product rule. I can calculate the tensor covariant derivative and prove things about it, but I still don't understand what it *is*.

  2. jcsd
  3. May 18, 2008 #2
    Basic Tensor Understanding

    There is a site at NASA, that is a introduction to tensor analysis. It starts with scalars, vectors, dyads ...etc. It is an excellent paper to understand what is really going on with tensors, and its free. It also has co. and contra. variant tensors.

    What a self promoting site. I cannot post the URL, because I have to make 15 posts or more. I am just trying to help someone. Thats what happens when a site starts to go commercial (Sci. Amer.). Contact me and I will e-mail the address.
  4. May 18, 2008 #3


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    Gold Member

    well, you can't blame a site which ends with .com of being commercial.
  5. May 18, 2008 #4
    I googled nasa tensor analysis, is this it:

  6. May 18, 2008 #5
    I'm reading this pdf and so far it is rocking hard. nice.
  7. May 18, 2008 #6
    I sent you the whole name. It is a little different, but you might have the same one, or a variant.
  8. May 18, 2008 #7
  9. May 18, 2008 #8
    Your welcome. It is kind of like all the nuts and bolts you cannot get unless you get a really great teacher. It is real basic stuff, but I promise you will learn tensors and really understand what is going on at the root level.
  10. May 18, 2008 #9
    I hope so. Right now working with tensors seems like a game you play by manipulating symbols according to random rules, although that is changing somewhat as I am reading the first pdf. After that, I'll get to the second pdf, and hopefully I'll be good after that.
  11. May 18, 2008 #10

    Forgot to tell you. After you read the pdf from nasa, get the schaums outline "Tensor Calculus", after those two things you will have no problem following any tensor book.

    GOOD LUCK !!!!
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