## 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!

1. feldy90

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

2. feldy90

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

3. vf321

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

4. vf321

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

5. feldy90

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

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

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

8. feldy90

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

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

10. vf321

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

11. feldy90

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

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

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

14. UnkleRhaukus

could this $A_{ij,i}$ mean this $A_{ij} , A_{ii}$

15. feldy90

Ummm... Yeah, potentially? Where $A_{ii}=A_{11}+A_{22}$