Results 1 to 3 of 3

Math Help - Potential function

  1. #1
    Super Member
    Joined
    Jun 2008
    Posts
    829

    Potential function

    Find a potential function

    F(x,y,z) = (yz)i + (xz+z)j + (xy+y-1)k

    My solution:

    rotF = [(x+1)-(x+1)]i - [y-y]j + [z-z]k
    rotF = (0,0,0) is conservative

    \frac{ \partial \phi}{ \partial x} = yz
    \phi (x,y) = yz + f(y)
    z + f'(y) = \frac{ \partial \phi}{ \partial y}
    f'(y) = xz ==> f(y) = xyz

    \phi (x,y,z) = yz + xyz + f(z)
    y + xy + f'(z) = \frac{ \partial \phi}{ \partial z}
    y + xy + f'(z) = xy +y -1
    f'(z) = -1 ==> f(z) = -1 + k

    Potential function:
    \phi (x,y,z) = yz + xyz -1 + k

    Correct ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    No her I'm using f for the potential fn and d/dx etc are partial derivatives

    in your first integration f = xyz + h(y,z) not yz

    df/dy = xz + dh/dy = xz +z

    h = yz + g(z)

    f= xyz + yz +g(z)

    df/dz = xy+y +g ' (z) = xy + y -1

    g(z) = -z

    f= xyz + y z - z

    You can always check by taking grad(f)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Ok. Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Potential Function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 3rd 2010, 12:09 PM
  2. potential function
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 5th 2009, 05:27 PM
  3. Potential Function...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 20th 2009, 03:09 AM
  4. corresponding potential function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 9th 2008, 06:55 PM
  5. Potential of a function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 28th 2007, 05:45 PM

Search Tags


/mathhelpforum @mathhelpforum