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Thread: Jacobian Matrix and differential equation

  1. #1
    Senior Member x3bnm's Avatar
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    Jacobian Matrix and differential equation

    Consider the function f : ℝ2 → ℝ2 given by
    Then we have
    and
    and the Jacobian matrix of F is
    and the Jacobian determinant is



    I know how to find Jacobian Matrix and its determinant.

    How can I use Jacobian's in differential equations? Is it possible to give an example with a differential equation?
    Last edited by x3bnm; Jul 19th 2018 at 10:30 AM.
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  2. #2
    MHF Contributor
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    Re: Jacobian Matrix and differential equation

    This is literally Example #1 in the Wikipedia article on Jacobian matrices. Is that where you got it from? Because if you read examples 2 through 4, it gives examples of how it is possible to use.
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  3. #3
    Senior Member x3bnm's Avatar
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    Re: Jacobian Matrix and differential equation

    Quote Originally Posted by SlipEternal View Post
    This is literally Example #1 in the Wikipedia article on Jacobian matrices. Is that where you got it from? Because if you read examples 2 through 4, it gives examples of how it is possible to use.
    But I got it from wikipedia. But couldn't I use it to find the solutions of certain differential equations?
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  4. #4
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    Re: Jacobian Matrix and differential equation

    What differential equations are you trying to use it for? You chose the one example where they did not show how to use the Jacobian, but ignored the two examples where they show it is used for a change of coordinates?
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