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Math Help - Partial derivatives

  1. #1
    Junior Member
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    Jan 2010
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    Partial derivatives

    Near what points (r,s) can the transformation
    x = r^2 + 2s
    y = s^2 - 2r
    be solved for r and s in terms of x and y

    Find \frac{\delta r}{\delta x} , \frac{\delta r}{\delta y}, \frac{\delta s}{\delta x}, \frac{\delta s}{\delta y} when (x,y,r,s)=(0,0,0,0)
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  2. #2
    Senior Member
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    The Jacobian of the transformation (r,s) \mapsto (r^2+2s, s^2 - 2r) is 4(rs+1) which vanishes iff rs=-1....
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