1. Limited time only! Sign up for a free 30min personal 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!

Exact differentials

  1. Jan 29, 2013 #1


    User Avatar
    Homework Helper

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

    Let R be a connected open region ( in the plane ). Suppose that F = (M,N) is a vector function defined on R and is such that for any ( piecewise smooth ) curve C in R :

    [itex]\int_C Fdp[/itex]

    depends on only the endpoints of C ( that is, any two curves from P1 to P2 in R give the same value for the integral).

    Prove that there exists a function u(x,y) defined on R such that ∇u = F.

    ( i.e ux = M and uy = N )

    2. Relevant equations

    Err I think this may have to do with simply connected regions?

    3. The attempt at a solution

    I'm not quite sure where to start with this one? I'm having trouble seeing how the info provided leads to what I need.

    I think it has to do with if R is a simply connected open region and Mdx + Ndy is such that My = Nx in R, then the differential is exact.

    Any push in the right direction would be great.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted