PDE constrained to a curve


by Sunfire
Tags: constrained, curve
Sunfire
Sunfire is offline
#1
Jul2-13, 10:31 AM
P: 177
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?
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Khashishi
Khashishi is offline
#2
Jul3-13, 05:52 PM
P: 833
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}##
Sunfire
Sunfire is offline
#3
Jul3-13, 08:06 PM
P: 177
Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.


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