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Math Help - Polar Coordinates

  1. #1
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    Polar Coordinates

    Let (x,y) be the common coordinates of R^{2} and V=R^{2}-\{(x,0):x\le 0\}. On V the polar coordinates are defined unambiguously for 0<\theta<2\pi. Find \frac{\partial}{\partial{r}}, \frac{\partial}{\partial{\theta}}. Find the relationship between these vectors and \frac{\partial}{\partial{x}}|, \frac{\partial}{\partial{y}}|.
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  2. #2
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    Quote Originally Posted by Ricko View Post
    Let (x,y) be the common coordinates of R^{2} and V=R^{2}-\{(x,0):x\le 0\}. On V the polar coordinates are defined unambiguously for 0<\theta<2\pi. Find \frac{\partial}{\partial{r}}, \frac{\partial}{\partial{\theta}}. Find the relationship between these vectors and \frac{\partial}{\partial{x}}|, \frac{\partial}{\partial{y}}|.
    1. By "common coordinates" I think you mean "Cartesian Coordinates"

    2. I don't know what the "|" is in \frac{\partial }{\partial x}| and  \frac{\partial }{\partial y}|

    3. If you mean the partial derivatives, use the chain rule: \frac{\partial U}{\partial r}= \frac{\partial x}{\partial r}\frac{\partial U}{\partial x}+ \frac{\partial y}{\partial r}\frac{\partial U}{\partial y}.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    1. By "common coordinates" I think you mean "Cartesian Coordinates"

    2. I don't know what the "|" is in \frac{\partial }{\partial x}| and  \frac{\partial }{\partial y}|

    3. If you mean the partial derivatives, use the chain rule: \frac{\partial U}{\partial r}= \frac{\partial x}{\partial r}\frac{\partial U}{\partial x}+ \frac{\partial y}{\partial r}\frac{\partial U}{\partial y}.
    Isn't common coordinates a reference to overlap maps?
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