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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!
 one year ago
 one year 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!
 one year ago
 one year ago

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feldy90Best ResponseYou've already chosen the best response.0
\[A_{ij} = x_ix_j^3+3x_1x_2\delta_{ij}\] calculate \[A_{ij,i}\] is what I mean
 one year ago

feldy90Best ResponseYou've already chosen the best response.0
Not looking for an answer, just what the question is asking. Thanks.
 one year ago

vf321Best ResponseYou've already chosen the best response.1
It's notation used for partial differentiation. Inside first.
 one year ago

vf321Best ResponseYou've already chosen the best response.1
\[f_{x,y}=\delta\frac{\delta f}{\delta x}/\delta y\] You know, chain rule and all that fun stuff....
 one year ago

feldy90Best ResponseYou've already chosen the best response.0
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?
 one year ago

vf321Best ResponseYou've already chosen the best response.1
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...
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Unless it means dA/d(ij) which is possible but unlikely.
 one year ago

feldy90Best ResponseYou've already chosen the best response.0
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\[A_{kl,kl}\]"
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Hmmm.. what course are you taking for this? It could be a matrixrelated problem...
 one year ago

vf321Best ResponseYou've already chosen the best response.1
and just to clarify the delta in there is that delta as in partial d or delta as in deltaepsilon delta?
 one year ago

feldy90Best ResponseYou've already chosen the best response.0
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
 one year ago

vf321Best ResponseYou've already chosen the best response.1
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.
 one year ago

feldy90Best ResponseYou've already chosen the best response.0
Thanks so much for your help  much appreciated anyway :)
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
could this \[A_{ij,i}\] mean this \[A_{ij} , A_{ii}\]
 one year ago

feldy90Best ResponseYou've already chosen the best response.0
Ummm... Yeah, potentially? Where \[A_{ii}=A_{11}+A_{22}\]
 one year ago
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