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A failing in 3d gradients?

  1. Sep 8, 2014 #1
    So my question is regarding the gradient of a function. Suppose we have a function expressed In cylindrical coordinates. Its expressed as z=rcos2@

    I expressed the equation in cylindrical, but for the sake of my logic I'll now talk about it in cartesian. It appears that dz/dx and dz/dy at the origin are both equal to one, and so the gradient would imply (back into cylindrical coordinates) dz\Dr at the 45 degree angle is not what the graph implies, What am I missing here?

    It seems to me that d(dz/ dr) \d@ is still valid as a gradient?

    Isn't the argument of the gradient in cartesian that dz/dy should not change much over small changes in x, and yet this is not true in this example.
    Last edited: Sep 8, 2014
  2. jcsd
  3. Sep 12, 2014 #2


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  4. Sep 12, 2014 #3


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    The gradient, whether in one or several variables, is a derivative, not a second derivative, like your "d(dz/dr)/d@".
  5. Sep 12, 2014 #4


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    If I understood correctly, this is true only when the gradient itself is continuous.
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