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    Solving a vector equation which seems to be indeterminate.

    Makes sense. Now I have |B|. To get the components of \vec{B}, I can use 0 = A_{x} B_{x} + A_{y}B_{y}+ A_{z}B_{z} and 0 = C_{x} B_{x} + C_{y}B_{y}+ C_{z}B_{z}, and B^{2} = B_{x}^{2} + B_{y}^{2} + B_{z}^{2} . Does that sound right?
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    Solving a vector equation which seems to be indeterminate.

    I have a vector equation: \vec{A} \times \vec{B} = \vec{C} . \vec{A} and \vec{C} are known, and \vec{B} must be determined. However, upon trying to use Cramer's rule to solve the system of three equations, I find that the determinant we need is zero. I know now that I need to choose a...
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    Vector calculus identity

    Yes, but using the Levi-Civita symbol will essentially mean writing out the components, and I was trying to prove it without doing that...
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    Vector calculus identity

    How is del (u . u) = |u|^2 (del) ?
  5. P

    Vector calculus identity

    Yes I have, but that doesn't give me the 1/2 in the first term .....
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    Vector calculus identity

    Can someone help me prove the identity \ u \times (\nabla \times u) = \nabla(u^2 /2) - (u.\nabla)u without having to write it out in components?
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    I have a function

    After you click 'preview', refresh the page - it should now show you what you typed. This is a known issue on these forums.
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    Commutation of differentiation and averaging operations

    Here's my definition of temporal average - <f(t,x)> = \stackrel{lim}{T\rightarrow\infty} \frac{1}{T} \int_{t_{0}}^{t_{0}+T} f(t,x) dt And it's all making even less sense to me now. With this definition, <f(t,x)> is...
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    Commutation of differentiation and averaging operations

    That's it actually. But all the math texts I saw move differentiation past the integral sign only when the two involve independent variables. Is there a rigorous justification for doing it when both the differentiation and integration involve the same variable? Edit - I just cant get the latex...
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    Commutation of differentiation and averaging operations

    I've been studying Turbulence, and there's a lot of averaging of differential equations involved. The books I've seen remark offhandedly that differentiation and averaging commute for eg. < \frac{df}{dt} > = \frac{d<f>}{dt} Here < > is temporal averaging. If...
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