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When he goes on the road, he travels with a laptop, iPod and sometimes a Nintendo DS and a Sony PlayStation Portable.

Well, we could use it and then subtract, but I was just going to say that ndS is actually the opposite of this.

Double integral over a surface of F dot n dS is going to be --What are we going to do?

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We said the line integral of F dot n ds is actually the line integral of - Q dx P dy.

So, we need to set up the flux integral for a vector field dot ndS.

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Displays the status of your connection to the NDS container.

We need to know what ndS is. Well, fortunately for us, we know that the top face is going to be the graph of some function of x and y.

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Well, I am going to give you another way ndS to think geometrically about n dS.

Sets the selected NDS container as the current context .

So, we should be able to get ndS using the same method, negative partial Now, there's a small catch.

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Double integral of f dot n dS of a closed surface S.

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We formed the flux integral that was a line integral F dot nds.

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See, if you take this convention then the z component of n dS is positive.

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So, we've seen a formula for ndS in this kind of situation, OK?

We have seen that ndS, sorry, so, just to remind you this is the graph of a function z equals z2 of x, y.

Well, we've seen formulas for ndS in various settings.

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Flux is integral F dot n ds, and that one corresponds to summing the normal component of a vector field.

Namely, that becomes the double integral over that surface S of curl F, ndS which I will write as dell cross F dot n dS.

We need to figure out how to ndS express n dS in terms of du and dv.

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You just find a formula for ndS dot product, substitute, evaluate.

OK. Let's look at yet another last way of finding n dS.

ndS So, how do I get ndS in that case?

And, once you have a formula for ndS, that will relate ndS to maybe dx dy, or something else.

In our daily lif, war dalling with different kinds of poll, no matter at hom, in school, or at som other placs. vryon nds hlp, I think.

And so n dS is this cross-product times du dv up to sign.

I think that is enough formulas for n dS.

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