1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

PDE constrained to a curve

  1. Jul 2, 2013 #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. Jul 3, 2013 #2

    Khashishi

    User Avatar
    Science Advisor

    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. Jul 3, 2013 #3
    Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: PDE constrained to a curve
  1. PDE solution (Replies: 5)

  2. Constrained motion (Replies: 1)

  3. Solving PDE (Replies: 0)

Loading...