Question

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!

Answer 1

\[A_{ij} = x_ix_j^3+3x_1x_2\delta_{ij}\] calculate \[A_{ij,i}\] is what I mean

Answer 2

Not looking for an answer, just what the question is asking. Thanks.

Answer 3

It's notation used for partial differentiation. Inside first.

Answer 4

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

Answer 5

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?

Answer 6

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...

Answer 7

Unless it means dA/d(ij) which is possible but unlikely.

Answer 8

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\[A_{kl,kl}\]"

Answer 9

Hmmm.. what course are you taking for this? It could be a matrix-related problem...

Answer 10

and just to clarify the delta in there is that delta as in partial d or delta as in delta-epsilon delta?

Answer 11

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

Answer 12

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.

Answer 13

Thanks so much for your help - much appreciated anyway :)

Answer 14

could this
\[A_{ij,i}\]
mean this
\[A_{ij} , A_{ii}\]

Answer 15

Ummm... Yeah, potentially? Where \[A_{ii}=A_{11}+A_{22}\]