Results 1 to 3 of 3

Math Help - Question involving Jacobian.

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    6

    Post Question involving Jacobian.

    The equations:
    u^2 + v^2 + xy - x^2 + y^2 = 5
    vxy - y^2 = 1
    Check the Jacobian condition at the point (x,y,u,v) = (1,1,0,2) and show that this allows x and y to be defined implicitly as functions of u and v. At this point, compute the Jacobian D(x,y)/D(u,v).


    Ok, a few problems with this one.
    1) I don't know what the Jacobian condition is.
    2) I don't know how to show that x and y are functions of u and v.
    3) I'm still iffy with Jacobians and I'm not sure how to find the Jacobian matrix.


    So, any tips to help me through this number?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,346
    Thanks
    29
    Quote Originally Posted by bleepbloop View Post
    The equations:
    u^2 + v^2 + xy - x^2 + y^2 = 5
    vxy - y^2 = 1
    Check the Jacobian condition at the point (x,y,u,v) = (1,1,0,2) and show that this allows x and y to be defined implicitly as functions of u and v. At this point, compute the Jacobian D(x,y)/D(u,v).


    Ok, a few problems with this one.
    1) I don't know what the Jacobian condition is.
    2) I don't know how to show that x and y are functions of u and v.
    3) I'm still iffy with Jacobians and I'm not sure how to find the Jacobian matrix.


    So, any tips to help me through this number?
    If x = x(u,v)\;\;y=y(u,v) the Jacobian is defined as

    <br />
\frac{\partial (x,y)}{\partial (u,v)} = \begin{array}{| c c |}x_u & x_v\\y_u&y_v\end{array}

    where subscripts denote partial differentiation and | \cdot| a determinant. Calculate your derivatives implicitly, substitute into the jacobian, then evaluate at your point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2009
    Posts
    6
    Quote Originally Posted by danny arrigo View Post
    If x = x(u,v)\;\;y=y(u,v) the Jacobian is defined as

    <br />
\frac{\partial (x,y)}{\partial (u,v)} = \begin{array}{| c c |}x_u & x_v\\y_u&y_v\end{array}

    where subscripts denote partial differentiation and | \cdot| a determinant. Calculate your derivatives implicitly, substitute into the jacobian, then evaluate at your point.
    Thanks, but it tells me to find the Jacobian condition (what is this?) and to show how this implies that x and y are functions of u and v before going on to the Jacobian matrix.
    How do I do these first two parts?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: December 7th 2011, 04:00 PM
  2. Jacobian determinant question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 23rd 2010, 12:32 AM
  3. Probability question involving (A given B type question )
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 9th 2009, 09:08 AM
  4. Replies: 19
    Last Post: October 19th 2009, 05:10 PM
  5. Jacobian involving Quaternions
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 9th 2009, 10:17 AM

Search Tags


/mathhelpforum @mathhelpforum