PDE constrained to a curve

  1. Hello folks,

    If we have the expression, say

    [itex]\frac{∂f}{∂r}[/itex]+[itex]\frac{∂f}{∂θ}[/itex], am I allowed to change it to

    [itex]\frac{df}{dr}[/itex]+[itex]\frac{df}{dr}[/itex][itex]\frac{dr}{dθ}[/itex],

    if "f" is constrained to the curve r=r(θ).

    My reasoning is that since the curve equation is known, then f does not really depend on the angle θ, but only on r (and r is a function of the angle, kind of a compound function).

    Does this make sense?
     
  2. jcsd
  3. This seems right conceptually, but notationally, some of those should be partial derivatives.
    ##\frac{\partial f}{\partial r} + \frac{\partial f}{\partial r} \frac{dr}{d\theta} = \frac{df}{dr}##
     
  4. Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.
     
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