Results 1 to 2 of 2

Math Help - Surface Integral

  1. #1
    Junior Member
    Joined
    Nov 2011
    From
    Karachi
    Posts
    36

    Surface Integral

    What's the difference between a surface integral with an S written underneath it and the one with two ∫ signs enclosed with a circle?

    Is a surface integral always with respect to the change in area (i.e. it is just a special case of integration where we integrate with respect to change in area), and we have named that case a surface integral?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2014
    From
    Dallas, Texas
    Posts
    17
    Thanks
    5

    Re: Surface Integral

    When there is a circle around the integral signs that means that $S$ is a closed surface. In fact a surface integral is a special case of integrating what is called a differential form. In the case of a surface integral we are integrating what is known as a 2-form: for a line integral we integrate a 1-form and in the case of an ordinary integral of a function we are integrating a 0-form. Indeed there are higher forms that can be integrated such as in volume integrals (integrating a 3-form). Now to directly answer your question: yes surface integrals always sum differential area elements.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Surface Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 9th 2013, 06:28 AM
  2. Convert line integral to surface integral
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 2nd 2013, 03:18 PM
  3. Volume integral to a surface integral ... divergence theorem
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: October 7th 2010, 06:11 PM
  4. Surface integral.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 19th 2010, 04:22 AM
  5. Surface Integral Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 14th 2008, 03:13 AM

Search Tags


/mathhelpforum @mathhelpforum