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Vector Analysis Resources

  1. Jul 13, 2009 #1
    So here I am, trying to learn vector analysis (vector calculus, call it what you want) and I'm all but befuddled by the number of ways to present the topic. I'm looking for a resource (preferably free) that expands on:

    Lame coefficients / scale factors (the same thing, right?)
    Metric coefficients
    Forms (maybe?)
    Generalized Stokes' Theorem
    Jacobian matrix

    Basically, my problem is this: my professor introduced scale coefficients without explaining how to calculate them, and in trying to learn it by myself, I stumbled upon all sorts of confusing and/or revealing generalizations. Unfortunately, I don't understand how they fit together.

    For example:
    - I know how to calculate the Jacobian given a transformation
    - I know how to derive div/grad/curl operators for orthogonal coordinate systems from reading the Appendix of Griffith's Electrodynamics. These forms depend on scale factors, which Griffiths, although including them, never explains how to find them or even what they really *are*.
    - I understand, to a degree, where scale factors and metric coefficients come from, from reading "Geometrical Vectors" and trying to understand wikipedia.
    - Wikipedia sucks.

    Is there anything that just gives the briefest (and I mean briefest) summary of how to compute these factors given a general curvlinear coordinate system? I can handle a sentence or two explaining the steps, but I really just need some worked examples. I'm also short on time! :)

    Thanks!
     
  2. jcsd
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