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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 [tex]\frac{d^{2}u}{dt^{2}}[/tex] which equals X''Y
Or Ux for [tex]\frac{du}{dt}[/tex] 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 [tex]\frac{d^{2}u}{dt^{2}}[/tex] which equals X''Y
Or Ux for [tex]\frac{du}{dt}[/tex] which equals X'Y

I think you meant
Uxx for [tex]\frac{\partial^{2}u}{\partial x^{2}}[/tex]
or
Ux for [tex]\frac{\partial u}{\partial x}[/tex]

Quote:

But what about U'x
Out of context, I would take that to mean [tex]\frac{d}{dt} \left(\frac{\partial u}{\partial x}\right)[/tex], but the context might indicate it meant something different. (The difference between [tex]d[/tex] and [tex]\partial[/tex] 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 [tex]\frac{\partial^{2}u}{\partial x^{2}}[/tex]
or
Ux for [tex]\frac{\partial u}{\partial x}[/tex]



Out of context, I would take that to mean [tex]\frac{d}{dt} \left(\frac{\partial u}{\partial x}\right)[/tex], but the context might indicate it meant something different. (The difference between [tex]d[/tex] and [tex]\partial[/tex] 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: [tex]U^{'}_{x}=U^{'}_{y}+U[/tex]


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