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Homework Help: Difference between dS and ds̄

  1. Dec 1, 2011 #1
    Difference between "dS" and "ds̄"

    http://img268.imageshack.us/img268/126/skjermbilde20111201kl71.png [Broken]

    I often see theorems such as the one above in my coursework, but I do not actually understand the difference between "dS" and "ds̄". I presume, because the latter has a "hat," that the latter also has something to do with vectors. So what's the difference between these two differential distances?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 1, 2011 #2


    Staff: Mentor

    Re: Difference between "dS" and "ds̄"

    The dS on the left is a vector, an increment of some vector S (looks sort of like the integral for work). The one on the right has dS as a scalar. The integrand here is the dot product of two vectors, which results in a scalar.
    Last edited by a moderator: May 5, 2017
  4. Dec 1, 2011 #3

    Ray Vickson

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    Re: Difference between "dS" and "ds̄"

    [itex] d\vec{S}[/itex] is the vector whose direction is [itex]\vec{n}[/itex] and whose magnitude is [itex] dS [/itex], so, in fact, we have [tex] d\vec{S} = \vec{n} dS. [/tex]

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