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-   -   Notation for separable partial differential equations (http://www.physicsforums.com/showthread.php?t=454514)

 frozenguy Dec6-10 11:59 PM

Notation for separable partial differential equations

Hey.. I ran across some problems and the notation used is a little different from what I've seen before.

considering U(x,y)=X(x)Y(y)
Sometimes I'll see Uxx for $$\frac{d^{2}u}{dt^{2}}$$ which equals X''Y
Or Ux for $$\frac{du}{dt}$$ which equals X'Y

But what about U'x

Is that a redundant way of saying the partial derivative of U with respect to x?

Or is it saying the derivative of the partial derivative of U with respect to x?

As I originally read it, I considered it X'Y, but now I'm wondering if maybe its X"Y.

Thanks!

 AlephZero Dec7-10 10:08 AM

Re: Notation for separable partial differential equations

Quote:
 Quote by frozenguy (Post 3023958) Hey.. I ran across some problems and the notation used is a little different from what I've seen before. considering U(x,y)=X(x)Y(y) Sometimes I'll see Uxx for $$\frac{d^{2}u}{dt^{2}}$$ which equals X''Y Or Ux for $$\frac{du}{dt}$$ which equals X'Y
I think you meant
Uxx for $$\frac{\partial^{2}u}{\partial x^{2}}$$
or
Ux for $$\frac{\partial u}{\partial x}$$

Quote:
 But what about U'x
Out of context, I would take that to mean $$\frac{d}{dt} \left(\frac{\partial u}{\partial x}\right)$$, but the context might indicate it meant something different. (The difference between $$d$$ and $$\partial$$ is not a typo.)

 frozenguy Dec7-10 07:19 PM

Re: Notation for separable partial differential equations

Quote:
 Quote by AlephZero (Post 3024644) I think you meant Uxx for $$\frac{\partial^{2}u}{\partial x^{2}}$$ or Ux for $$\frac{\partial u}{\partial x}$$ Out of context, I would take that to mean $$\frac{d}{dt} \left(\frac{\partial u}{\partial x}\right)$$, but the context might indicate it meant something different. (The difference between $$d$$ and $$\partial$$ is not a typo.)
Yes that was a bad typo I'm sorry. Glad you knew what I was talking about.

The context would be partial differential equations using separation of variables.

For example: $$U^{'}_{x}=U^{'}_{y}+U$$

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