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Partial differential equations

Hi there everyone I was wondering if someone could help me! I am trying to understand the partial differentiation that has been carried out in the paper I am looking at

http://ars.els-cdn.com/content/image/1- ... 5-si13.gif

I don't really understand how they remove the summation signs by manipulating the I and j's! Also I was wondering if you could help me adjust this slightly for my data which is 3D and so I would need to carry out the derivative over I, j and k instead of just I and j?

Any help is very much appreciated!
Original post by branny12000
Hi there everyone I was wondering if someone could help me! I am trying to understand the partial differentiation that has been carried out in the paper I am looking at

http://ars.els-cdn.com/content/image/1- ... 5-si13.gif

I don't really understand how they remove the summation signs by manipulating the I and j's! Also I was wondering if you could help me adjust this slightly for my data which is 3D and so I would need to carry out the derivative over I, j and k instead of just I and j?

Any help is very much appreciated!

The first line looks dodgy. On the left hand side you have a derivative to be evaluated at (i,j) and on the right hand side you sum over (i,j). It isn't clear from this calculation what i,j are meant to be. I think that we will need more context to be able to properly answer this question.

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