1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

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

    User Avatar
    Science Advisor
    Homework Helper

    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]

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook