1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Vector calculus question.

  1. Nov 21, 2008 #1
    1. The problem statement, all variables and given/known data

    Let S be the surface given by the graph z = 4 - x2 - y2 above the xy-plane (that it is, where z [tex]\geq[/tex] 0) with downward pointing normal, and let

    F (x,y,z) = xcosz i - ycosz j + (x2 + y2 ) k

    Compute [tex]\oint\oints[/tex][tex]\oint[/tex]s F dS. (F has a downward pointing normal)

    (Hint: Its easy to see that div F = 0 on all R3. This implies that there exists a vector field G such that F = Curl G, although it doesnt tell you what G is)



    2. Relevant equations

    z = 4 - x2 - y2 above the xy-plane (that it is, where z [tex]\geq[/tex] 0) with downward pointing normal

    F (x,y,z) = xcosz i - ycosz j + (x2 + y2 ) k

    Compute [tex]\oint\oints[/tex][tex]\oint[/tex]s F dS. (F has a downward pointing normal)

    3. The attempt at a solution

    Im getting throw off a bit by the hint. I know its something to do with the surface not being defined around the origin but thats about it.

    1. The problem statement, all variables and given/known data

    See above

    2. Relevant equations

    How do I solve this?!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 21, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Looks to me like the hint is suggesting you use Stokes' theorem:
    [tex]\int \vec{G}\cdot\d\vec{r}= \int\int \nabla G\cdot d\vec{S}[/tex]
     
  4. Nov 21, 2008 #3
    Right, but how do I compute this? My daughter hasnt gone past Green's theorem yet in class....I saw this problem on her homework but she couldnt solve it. I can help her and know some Multivariable calculus (but not vector calculus). I want to help her get through this. I would really appreciate it if someone spelt out the solution for me. So I could learn this and help her out with this. I hope thats not an unreasonable request :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Vector calculus question.
  1. Vector calculus question (Replies: 30)

Loading...