# PDE constrained to a curve

by Sunfire
Tags: constrained, curve
 P: 177 Hello folks, If we have the expression, say $\frac{∂f}{∂r}$+$\frac{∂f}{∂θ}$, am I allowed to change it to $\frac{df}{dr}$+$\frac{df}{dr}$$\frac{dr}{dθ}$, 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?
 P: 832 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}##
 P: 177 Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.

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