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Thread: laplace equation in polar coordinates

  1. #1
    Junior Member
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    laplace equation in polar coordinates

    Hi members,

    in changin from cartesian to polar coordinates they use:

    x=r*cos(phi)
    y=r*sin(phi)
    then using the chain rule delta u/delta r=delta u/delta x.delta x/delta r+delta u/delta y.delta y/delta r
    My question:
    Delta x/delta r=cos(phi) (here delta means partial derivative)

    Is it delta x=delta r*cos(phi).How is it calculated????

    Thank you
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  2. #2
    MHF Contributor

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    Re: laplace equation in polar coordinates

    You seem to be wanting to go from $\frac{\partial x}{\partial r}= cos(\phi)$ to $\partial x= \partial r cos(\phi)$. You can't do that! $\frac{\partial x}{\partial r}$ is defined as single quantity, not as a fraction.
    (In ordinary derivatives, $y'= \frac{dy}{dx}$ is also defined as a single quantity but then we define "differentials" so that we can treat it as a fraction, $dy= y' dx$, but we cannot do that with partial derivatives.)
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  3. #3
    MHF Contributor
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    Re: laplace equation in polar coordinates

    a quick application of google works wonders....

    https://www.math.ucdavis.edu/~saito/.../polar-lap.pdf
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