Results 1 to 3 of 3

Math Help - Conservative field?

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    28

    Conservative field?

    Hi.

    Just checked my answer on a question from my workbook on line integrals. Almost nailed it but not quite.

    Question is this.

    Verify that the following vectorfield is conservative and determine itīs "potential function" (Donīt know if itīs the correct translation but maybe youīll get it from my attempt)

    Conservative field?-picture-1.png

    I get an extra 2 in the answer and I donīt know why. This is extremely irritating as I get stuck with small problems. Takes a lot of time which I donīt have. So what did i miss?

    -WS
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    You are getting \varphi(x,y)=e^x \sin y + C_1(y)

    Now on one hand \frac{\partial \varphi}{\partial y} = e^x \cos y + C_1'(y)

    on the other hand \frac{\partial \varphi}{\partial y} = e^x \cos y

    therefore C_1'(y) = 0 which means that C_1(y) = C_1 and finally \varphi(x,y)=e^x \sin y + C_1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    28
    Yes of course. Thank you! I tried to follow the method from an example in my workbook mechanically without really understanding the procedure. I searched the web and found it easier to understand this with another notation for partial derivatives. But your explanation makes even more sense.

    -WS
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Conservative field?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 23rd 2011, 11:18 AM
  2. conservative scalar field?
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 29th 2010, 04:19 AM
  3. Conservative field
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 27th 2009, 02:07 PM
  4. Conservative field
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 26th 2009, 03:22 PM
  5. Conservative Vector Field!!!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 4th 2009, 08:26 AM

/mathhelpforum @mathhelpforum