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feldy90

  • 3 years ago

Notation help: what does a comma in a subscript mean? I am given A_ij and asked to calculate A_ij,i ... Something about differentiation? I can't remember. Any help would be great, thanks!

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  1. feldy90
    • 3 years ago
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    \[A_{ij} = x_ix_j^3+3x_1x_2\delta_{ij}\] calculate \[A_{ij,i}\] is what I mean

  2. feldy90
    • 3 years ago
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    Not looking for an answer, just what the question is asking. Thanks.

  3. vf321
    • 3 years ago
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    It's notation used for partial differentiation. Inside first.

  4. vf321
    • 3 years ago
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    \[f_{x,y}=\delta\frac{\delta f}{\delta x}/\delta y\] You know, chain rule and all that fun stuff....

  5. feldy90
    • 3 years ago
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    Woah okay... Maybe I do need help then! So the above question would work out to just be\[A_{ij,i}=x_i\]? Because every j term is counted as a constant? And the Kroneker delta would just be zero, because i/=j?

  6. vf321
    • 3 years ago
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    Well hang on. I don't get why your book or whatever wouldn't use A_i,j,i and not A_ij, i... This is for differential equations, right? That's where I'm getting the subscript convention...

  7. vf321
    • 3 years ago
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    Unless it means dA/d(ij) which is possible but unlikely.

  8. feldy90
    • 3 years ago
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    Yeah I'm assuming so? The question as I have it is: "For \[A_{ij}=x_ix_j^3+3x_1x_2\delta_{ij}\] (i,j=1,2) Calculate \[A_{ij,i} \]and\[A_{kl,kl}\]"

  9. vf321
    • 3 years ago
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    Hmmm.. what course are you taking for this? It could be a matrix-related problem...

  10. vf321
    • 3 years ago
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    and just to clarify the delta in there is that delta as in partial d or delta as in delta-epsilon delta?

  11. feldy90
    • 3 years ago
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    It's just called "Applied Mathematical Modelling" ... We did cover a few things on matrices in theis chapter, but not too in depth... I think the delta is the substitution tensor? \[\delta_{ij}=\left\{ \left(\begin{matrix}{1 'if' i=j} \\ {0 'if' i \neq j}\end{matrix}\right) \right\}\] Hmmm that didn't quite come out the way I wanted it, but basically the delta = 1 if i=j, and delta = 0 if i does not =j

  12. vf321
    • 3 years ago
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    Hmm... well when you say tensor it does make me think matrix... I'd love to help, but the general uses of subscripts are to identify partial derivatives or location in a matrix (x_1,1) means top left corner. It seems to me that the use of subscripts here is a convention defined in your book. Sorry.

  13. feldy90
    • 3 years ago
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    Thanks so much for your help - much appreciated anyway :)

  14. UnkleRhaukus
    • 3 years ago
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    could this \[A_{ij,i}\] mean this \[A_{ij} , A_{ii}\]

  15. feldy90
    • 3 years ago
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    Ummm... Yeah, potentially? Where \[A_{ii}=A_{11}+A_{22}\]

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