Notation for separable partial differential equations

  1. 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!
     
  2. jcsd
  3. AlephZero

    AlephZero 7,299
    Science Advisor
    Homework Helper

    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.)
     
    Last edited: Dec 7, 2010
  4. 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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