Divergence Theorem

[Kount]

It's about problem number 5 on this sheet. I tried to solve it on my own, but got stuck, so I looked at the solution.

The last line was the problem.

Why is it allowed to pull the \(\displaystyle \pm\)-sign out of the integral? How can I know that it's either plus or minus all the time and not changing while I integrate?

Thanks in advance!

 

[afrazer721]

It's about problem number 5 on this sheet. I tried to solve it on my own, but got stuck, so I looked at the solution.

The last line was the problem.

Why is it allowed to pull the \(\displaystyle \pm\)-sign out of the integral? How can I know that it's either plus or minus all the time and not changing while I integrate?

Thanks in advance!

I read up on fluorescence. The negative side of y-axis is pulled in the direction of the positive side of the x-axis to be plugged into the x-axis. It's the Laplacian first then the coruscating Divergence Theorem. The glaring apiculate form of dx and dy are seen.

Bacon is frying in a frying pan. Grease, melted fat, is coming at some point from the bacon. These points are called 'sources' and have positive divergence. After the cooked bacon is placed on Bounty paper towels(iso-surface), the paper towels are imbibed with grease and eventually for cleaning purposes discarded(n is outward unit normal to S). The absorbed grease gives rise to a velocity vector field...The plus-minus sign of the integral may experience a miscalculated representation due to concealment of fact, subreption. Thus, the author of the problem believes the plus-minus sign is plus only because the gradient curls even tighter.

These are my tentative thoughts on the Divergence Theorem and Laplacian.

"Both now and for always, I intend to hold fast to my belief in the hidden srength of the human spirit." Andrei Sakharov, physicist

 

[Kount]

What????

 

[srmichael]

I read up on fluorescence. The negative side of y-axis is pulled in the direction of the positive side of the x-axis to be plugged into the x-axis. It's the Laplacian first then the coruscating Divergence Theorem. The glaring apiculate form of dx and dy are seen.

Bacon is frying in a frying pan. Grease, melted fat, is coming at some point from the bacon. These points are called 'sources' and have positive divergence. After the cooked bacon is placed on Bounty paper towels(iso-surface), the paper towels are imbibed with grease and eventually for cleaning purposes discarded(n is outward unit normal to S). The absorbed grease gives rise to a velocity vector field...The plus-minus sign of the integral may experience a miscalculated representation due to concealment of fact, subreption. Thus, the author of the problem believes the plus-minus sign is plus only because the gradient curls even tighter.

These are my tentative thoughts on the Divergence Theorem and Laplacian.

"Both now and for always, I intend to hold fast to my belief in the hidden srength of the human spirit." Andrei Sakharov, physicist

:shock:

 

[HallsofIvy]

I'm afraid this board hasn't yet solved the problem of people who think it is a good joke to respond to a serious question with gibberish. It is, I expect, their way of showing contempt for mathematics or, indeed, anything that requires intelligence, work, and discipline.

In this case, you are asking about taking the \(\displaystyle \pm\) out of the integral? "\(\displaystyle \pm\)" just means either +1 or -1. Which ever happens to be the case, that is a constant and we can always take a constant out of the integral.