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    Hey the attachment below is the question I have been given. I have to be honest I have no idea what a metric is. I must have completely missed this part of my course. My problem is, as I don't know what they are, I can't tell if anything I read about them is relevant.

    Any help at all either with the question or an explanation of metrics would be GREATLY appreciated.

    I'm trying to revise for my exams and this has me completely confused.Name:  sevvarcalc.png
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    Update I think I know how to solve the question now, using what I found here, http://answers.yahoo.com/question/in...4121419AAzTxKC. The only part of the question I don't understand is the dr/du, dr/dv etc. What does the 'r' represent?

    My other problem is still that all this link gives me is an answer and does not really give me an explanation.
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    If you don't know what a metric is the term was probably introduced as terminology rather than stuff on metric tensors being covered. The  h_i are also called scale factors, which might be a more enlightening word to use. Two links with definitions that should help you:

    http://en.wikipedia.org/wiki/Curvili...ector_calculus

    http://www.phys.ufl.edu/courses/phy3...oordinates.pdf

    Oh and  \mathbf r = x \mathbf e_x + y\mathbf e_y + z\mathbf e_z where  \mathbf e_x, \mathbf e_y, \mathbf e_z are unit vectors in the x,y and z directions respectively.
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    (Original post by jb444)
    If you don't know what a metric is the term was probably introduced as terminology rather than stuff on metric tensors being covered. The  h_i are also called scale factors, which might be a more enlightening word to use. Two links with definitions that should help you:

    http://en.wikipedia.org/wiki/Curvili...ector_calculus

    http://www.phys.ufl.edu/courses/phy3...oordinates.pdf

    Oh and  \mathbf r = x \mathbf e_x + y\mathbf e_y + z\mathbf e_z where  \mathbf e_x, \mathbf e_y, \mathbf e_z are unit vectors in the x,y and z directions respectively.
    Okay thank you very very much . I'll check out those links that should help me greatly.

    Okay so how would I calculate r without knowing x,y and z. Or in the case of this question would I use u,v, and thi? In which case I am slightly confused as how could I work out e_u with [latex] 1/{h_u}dr/du[\latex] when the solution for dr/du would include eu?
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    You have

     \mathbf r = x \mathbf e_x + y\mathbf e_y + z\mathbf e_z

    so

     \mathbf r = uv\cos\phi \mathbf e_x + uv\sin\phi \mathbf e_y + \frac12 (u^2-v^2)\mathbf e_z

    Using this expression you can compute explicitly  \frac{\partial \mathbf r}{\partial u} etc, since the vectors \mathbf e_x ,\mathbf e_y, \mathbf e_z are fixed, so the expression depends only on  u,v,\phi.

    Then to get the unit vectors use the expressions given in the question.
 
 
 
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