# PDE constrained to a curve

1. Jul 2, 2013

### Sunfire

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?

2. Jul 3, 2013

### Khashishi

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. Jul 3, 2013

### Sunfire

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