Problem with the Divergence Theorem

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Discussion Overview

The discussion revolves around a homework problem related to the Divergence Theorem, specifically focusing on the evaluation of a triple integral and the divergence of a vector field. Participants are seeking clarification on their calculations and expressions, as well as addressing potential errors in the provided assignment.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about their calculation for part b) of the assignment and seeks validation of their derived expression for the triple integral.
  • Another participant suggests that the divergence should be 3r², indicating a potential correction to the original expression.
  • A participant points out that the original expression contains a discrepancy with the 2xy term, which should have opposite signs based on the vector field components.
  • One participant confirms their agreement with the divergence being 3r², aligning with another's earlier statement.
  • Concerns are raised about a possible mistake in part 3a), with a participant sharing their derived vector field and seeking confirmation from others.
  • Another participant humorously suggests that the lecturer may be embarrassed by the mistake, indicating a shared sentiment about the assignment's accuracy.

Areas of Agreement / Disagreement

Participants generally agree on the divergence being 3r², but there are multiple competing views regarding the correctness of the expressions and calculations for the homework problem. The discussion remains unresolved as participants continue to seek clarification and validation.

Contextual Notes

There are indications of potential errors in the original expressions and calculations, particularly concerning the divergence and the terms involved in the vector field. Participants express uncertainty about specific components and seek to clarify these issues without reaching a definitive resolution.

Claire84
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I was wondering if someone could give me a hand here with 2b) on the following link.
http://www.am.qub.ac.uk/users/j.mccann/teaching/ama102/2003/assignments/assign_8.pdf
For part a) I got it to be equal to 3x^2+3y^2+3z^2+2y-2xy, and I'm hoping that's right!

However, for part b) I can't seem to get the answer they're after at all. We haven't covered any examples of this in our lectures yet and we won't have any lectures before the homework has to be handed in due to May Day, so any help would be much appreciated. Just to make sure I started it off right, could you just check if this is correct or not (sorry, I'm no good with LaTex!)-

triple integral of (3r^2sin^2(theta)cos^2(f)+ 3r^2sin^3(theta)sin^2(f) + 3r^2cos^2(theta) + 2rsin(theta)sin(f) - 2r^2sin^2(theta)cos(f)sin)f))r^2sin(theta)drdfdtheta

where the integral with respect to r is within the limits 0 and a, with respect to f is 0 to 2pi and with respect to theta is 0 to pi (where f is the asimuthal angle or whatever it's called). I'd really appreciate if you could just ehck I've done that bit okay, because it'd be a bit pointless me running through it if the mistake was in the first line.

Btw, the answer I get at the end has an 8 on the numerator instead of a 12, so the answer isn't completely far out so I'm hoping it's just a wee mistake somewhere. Thanks! :smile:


Btw, sorry if this is posted in the wrong forum!
 
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The divergence should be 3r^(2). I'll look a bit further into this..
 
Ok:
If you go back to your vector field, you'll see that from both the j'th and k'th component, you will gain a 2xy term, but with opposite signs.
In your original expression, you've ended up with 2y-2xy instead
 
Ah so shold it look like this then-

3x^2 + 3y^2 + 3z^2 ?

Gah I can be so stupid with even the simplest things!

Thanks for helping btw! :smile:
 
That's what I got, too (3r^(2)).
 
Btw, for part 3a), that's a mistake, right? I mean I keep getting xi - yj + (-y^2 - x)k and I asked one of the phd students about it and they got the same but I just want to check before I email the lecturer about it...
 
Agreed, he'll be writhing in shame..
 
Hope that wasn't sarcasm there. :-p
 

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