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PDE constrained to a curve 
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#1
Jul213, 10:31 AM

P: 215

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
Jul313, 05:52 PM

P: 887

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}## 


#3
Jul313, 08:06 PM

P: 215

Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.



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