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I Gauss' Theorem -- Why two different notations are used?

  1. Sep 30, 2018 #1

    sams

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    In Mathematical Methods for Physicists, Sixth Edition, Page 60, Section 1.11, the Gauss' theorem is written as:
    Gauss' Theorem.PNG
    In Mathematical Methods for Physicists, Fifth Edition, Page 61, Section 1.11, the Gauss' theorem is written as:
    Gauss' Theorem 2.jpeg
    Kindly I would like to know please:
    1. What is the difference between the two relations?
    2. What does ##\partial{V}## in Equation (1.101a) stands for? In physics, I realized that ##\partial{V}## is usually not included when Gauss' theorem is used, why is that?

    Thanks a lot for your help...
     
    Last edited by a moderator: Oct 15, 2018 at 12:52 PM
  2. jcsd
  3. Sep 30, 2018 #2

    PeroK

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    Do these books not make their notation clear? The only difference is notational.

    ##\partial V## is sometimes used for the surface of a region ##V##. In the second equation, simply ##S## is used for the surface of the region ##V##.
     
  4. Sep 30, 2018 #3

    jedishrfu

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    The notation used by the sixth edition was to remind the reader that the left hand side is a double integral over the surface of the region and the right hand side is a triple integral over the volume of the region. They likely changed it as someone brought it to their attention or an editor schooled as a physicist took issue and decided it was best to change it.
     
  5. Oct 1, 2018 #4

    Svein

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  6. Oct 2, 2018 #5
    Usually un physics triple or double integrals $$\int \int$$ $$\int \int \int$$
    Are changed by only one simbol $$\int$$, so that is the same equation.

    The simbol $$\partial v$$ means that the integral Is computed on boundary superfice of $$v$$ or on boundary of $$v$$.
    $$\partial v=S$$
     
  7. Oct 13, 2018 at 1:21 PM #6

    sams

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    Thank you all for your help and for your explanations
     
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