- #1

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## Homework Statement

This is a coursework problem. I am having issues understanding the concepts on this one topic - divergence and how it relates to flux. I have attached screenshots that honestly give the best representation of my issue but I will set up the issue I am having none-the-less:

We are trying to find an equation for the divergence. He gives that div

**v**= lim τ->0 [itex]\frac{\oint

**v**dot d

**a**}{Δτ}[/itex]. So then he sets up a rectangular prism. He didn't go through this with us as he just posted in notes scanned. So

**v**is some vector function da is the normal area to the right plane. In the image he also puts a bunch of points. I guess he choose an x,y,z point contained in the rectangular prism (FIRST QUESTION: Does the x,y,z coordinate location matter? Could I have done it in one of the quarters of the shape rather than in the middle?). He then talks about how x,y,z vary in that right plane.

SECOND QUESTION: why does he say "Since we are going to be multiplying by Δx and Δz, any variation in x and z in these ranges will give rise to (Δx)^2 or (Δz)^2 terms, which we can ignore.

He then sets up

**v**dot d

**a**as the y component of it (parallel to the normal of that plane.

I think I should leave it there actually because I feel once I understand the second question, that will give me clues to what is going on. I have been trying to figure this out for quite sometime now and I am lost on how he went from the v-da to the stuff on page 22. If you look later on page 22 at the rectanglular prism that is sliced on a diagonal that is a homework problem we have to do (show that it doesn't matter what shape we choose). I want to try that on my own but I need to know how he set his up first. Any help would be greatly appreciated