# Homework Help: Understnding this index notation

1. Sep 4, 2016

### kajalschopra

1. The problem statement, all variables and given/known data
I shall be grateful if someone can help me understand this notation:

http://files.engineering.com/getfile.aspx?folder=340bee11-1ba4-49b2-9a31-1a747012d69b&file=1.gif

I know that this notation will finally/should finally give me the below six equations

But I do not know how to expand the above notation.

I have uploaded the imapge file to engineering.com as I couldn't upload it here
2. Relevant equations
As stated / described abov

3. The attempt at a solution

I know the answer but struggling o expand. Tried with notation/calculus but couldn't arrive at it.

2. Sep 4, 2016

### Mr-R

Fix $i$, $j$ and then run over $k$.
For example for $i=x$ and $j=y$ $$\epsilon_{xy,kk}=\epsilon_{xy,xx}+\epsilon_{xy,yy}+\epsilon_{xy,zz}$$
Where a comma denotes a partial derivative. ($A_{,x}=\frac{\partial A}{\partial x}$)
Hope this helps.

3. Sep 4, 2016

### kajalschopra

Sorry..but I'm not able to exactly get what you meant? I mean what do the "###" indicate. Didn't really what you meant by "fix and run over"

I know comma denotes a partial derivative but just not able to get the expansion

4. Sep 4, 2016

### Mr-R

You are not supposed to see those. Are you sure that your browser can render Latex?
I gave an example for you, but if your browser can't render it then there is no point of typing again. Please check that first.

5. Sep 4, 2016

### phinds

Here's what it should look like:

6. Sep 5, 2016

### kajalschopra

Thanks a lot. I have been reading about Einstein summation convention from here: http://mathworld.wolfram.com/EinsteinSummation.html

Thus, I have:

εij,kk + εkk,ij = εik,jkjk,ik

So, will I get 6 equations from the above?

I think, I will get 9 equations as per Einsteins summation convention?

To get the first equation,

1) To get the first equation, put i = x and j = x and sum over k (the repeated index)
2) To get the second equation , put i = x and j=y and sum over k
3) To get third equation put i = x and j=z and sum over k
4) To get the fourth equation put i =y and j=x and sum over k
5) To get the fifth equation put i =y and j=y and sum over k
6) To get the sixth equation put i =y and j=z and sum over k
7) To get the seventh equation put i =z and j=x and sum over k
8) To get the eigthh equation put i =z and j=y and sum over k
9) To get the ninth equation put i =z and j=z and sum over k

Will it give nine equations? for the above term?

7. Sep 7, 2016

### kajalschopra

I shall be grateful if someone can help with the above?