This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
(Moved from my talk page)
Thank you for your changes to divergence theorem. However, I have some remarks about links.
First, one should not link to plural, rather to singular, so it's got to be [[divergence]]s and not [[divergences]]. Second, you should wonder if links are actually needed, a link to sink does not make any sence in that article.
Third, one should check where the links point to. Instead of boundary one should link to [[boundary (topology)|boundary]]. Fourth, a link to " conservation law" should be instead conservation law, because, as you notice, those two words go together.
These are minor things, but it helps give value to the links. Thanks. Oleg Alexandrov ( talk) 10:38, 29 October 2005 (UTC)
By symmetry,
Why? -- Abdull 19:30, 2 June 2006 (UTC)
I have added a bit of clarification to the section for spherical symmetry. I was prompted by a change provided by 83.30.188.66 ( talk · contribs), which was aiming for clarity, but technically introduced an error. I hope the rewording I have now supplied makes it a bit clearer. Further suggestions very welcome. — Duae Quartunciae ( talk · cont) 11:48, 5 August 2007 (UTC)
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:48, 10 November 2007 (UTC)
Could somebody with the requisite mathematical expertise please fill this in?
I made dedicated articles for Gauss's law for magnetism and Gauss's law for gravity, and accordingly moved some material from here to those pages. (I went through and updated the links for hopefully all of the other wikipedia articles citing this material.) By the way, anyone interested in contributing to those articles is encouraged to do so. :-) -- Steve ( talk) 21:08, 1 April 2008 (UTC)
On the plus side, it helps people who only know a little calculus, and aren't familiar with the idea of one squiggly-integral sign denoting anything other than a one-dimensional integral. On the minus side, it makes equations harder to read and generally more cluttered. On the plus side, anyone who can understand it with one integral sign can understand it with three, but not necessarily vice-versa. On the minus side, I don't think any professional mathematician or physicist would write it this way (except maybe when they're writing introductory textbooks), and at least the physics articles I've seen on Wikipedia don't write it that way either.
Has anyone thought about this issue, pro and/or con? I have mixed feelings, myself. -- Steve ( talk) 21:07, 8 April 2008 (UTC)
I once (far far time ago) learned about other (of the many, Wikipedia should have a disambiguation page or something about this, its a serious issue) algorithm called "Gauss theorem", used for findings roots equations (of any power) when [independent coefficient]/[primary coefficient] is an integer by "trying" with different roots gotten by finding divisors of that division. How is this theorem called in Wikipedia-Other parts of the world other than my classroom? -- Me ( talk) 23:34, 19 September 2008 (UTC)
The condition of the div theorem says that F must be C1. How can the theorem be applied then for example, for , where G is a Green's function? Typically, Green's functions have a singularity, so they are not C1. Does this mean the divergence theorem can be extended? -- Janzz2k 17:21, 19 April 2007 (UTC)
The condition of the div theorem states that F must be C1. However, the derivative does not need to be continuous. This can be proven by decomposing the volumetric domain into subregions where the function is C1. It is readily seen that if the function is continuous, the terms corresponding to interior boundaries will cancel. —Preceding unsigned comment added by 128.115.27.10 ( talk) 17:22, 16 March 2011 (UTC)
Anyone interested to add something about application of Gauss's law in acoustics published in http://www.arxiv.com/abs/1104.0893 — Preceding unsigned comment added by 93.139.121.178 ( talk) 19:08, 30 May 2011 (UTC)
In my calculus book I remember that Green's theorem could be obtaneid as a particular case of Gauss theorem. I think all u had to was to remove one coordinate. — Preceding unsigned comment added by 85.18.50.180 ( talk) 11:50, 5 June 2011 (UTC)
Because this article is specifically about the divergence theorem and not about general Vector fields, I felt that the picture given in the example ( found here) had little to offer to a reader's understanding of the divergence theorem or the example. I've since rendered and inserted a replacement image with the example field plotted. Glosser.ca ( talk) 01:09, 5 November 2011 (UTC)
(Inspired by the Green Theorem comment above.)
What do people think about discussing the two-dimensional (or n-dimensional) case, instead of just 3D? I know we've decided in the past to leave all generalizations to the Stokes' theorem article, but looking at that article, it seems to me like Stokes' theorem is more abstract and more general and more complicated than just the straight generalization of the divergence theorem. In particular, non-mathematicians (e.g. engineers) may be interested in the 2D divergence theorem but would not be well served by the Stokes' theorem article. :-) -- Steve ( talk) 18:47, 5 June 2011 (UTC)
Sorry about the table in the 1st Example to complicate the markup, but the new template is gradually becoming popularized on WP, so a table was required to block the template integral expression and the lines of calculation tidily:
which translates to the mark-up: =(
:{| |- valign="top" | {{oiint | intsubscpt = <math>\scriptstyle S</math> | integrand = <math>\mathbf{F}\cdot\mathbf{n} \, dS</math> }} || || <math> \begin{align} &= \iiint\limits_W\left(\nabla\cdot\mathbf{F}\right) \, dV\\ &= 2\iiint\limits_W\left(1+y+z\right) \, dV\\ &= 2\iiint\limits_W \,dV + 2\iiint\limits_W y \,dV + 2\iiint\limits_W z \,dV. \end{align} </math> |}
F = q(E+v×B) ⇄ ∑ici 20:28, 2 April 2012 (UTC)
I've just been going over my notes from Maths, and I've noticed that the gauss integral doesn't specify a closed surface (). Can anyone confirm that it doesn't need the closed surface part? (sorry, can't figure out the double closed integral) —Preceding unsigned comment added by Jporteous ( talk • contribs) 14:33, 8 September 2008 (UTC)
Claiming it is corrected called something based on who gave the first rigorous proof is interjecting the author's opinion in how theorem's should be named. Fermat didn't prove Fermat's Last Theorem, Stokes didn't prove what we now call Stokes' Theorem in geometry, etc. If someone wants to include it being called something else that's fine, but saying one way is correct is an opinion which doesn't belong here. RyanEberhart ( talk) 19:50, 20 September 2012 (UTC)
Here is the text from the article: "Let's say I have a rigid container filled with some gas. If the gas starts to expand but the container does not expand, what has to happen? Since we assume that the container does not expand (it is rigid) but that the gas is expanding, then gas has to somehow leak out of the container. (Or I suppose the container could burst, but that counts as both gas leaking out of the container and the container expanding.)"
This is not true. If the gas expands, due to, perhaps, an increase in temperature, then the pressure in the container will rise, without the volume of the container necessarily changing. This is why things explode in the first place—the pressure builds up due to gas expansion (temperature increase) but gas cannot escape, leading to a pressure build-up and eventual explosion. I don't know enough math to suggest a better example, but this one is severely flawed.
24.60.252.143 ( talk) 15:57, 13 August 2014 (UTC)
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I'm not an expert on the topic, but could the article be improved by adding a proof? 50.39.171.4 ( talk) 19:33, 1 November 2018 (UTC)
In both given examples, you are using and . Since we are not used to it: Is this a standard notation for the unit vectors? — Preceding unsigned comment added by 129.27.232.39 ( talk) 10:28, 9 December 2018 (UTC)
I haven't been able to find a proof or reference for the divergence theorem for surfaces with piecewise smooth boundary. The reference provided does not mention boundary smoothness at all, nor does it provide any proof or references. Does anyone know of a proof in the piecewise smooth case, and if so can they add it? — Preceding unsigned comment added by 129.94.177.30 ( talk) 05:34, 7 January 2020 (UTC)
A statement and proof of the piecewise-smooth case in three dimensions can be found in this book. [1] Does this require a proof for an arbitrary number of dimensions? Or would this reference suffice? Benjamin Schulz ( talk) 23:12, 4 April 2020 (UTC)
The book "Calculus on manifolds - Spivak - 1968", on page 137, says the theorem is true for piecewise-smooth case. — Preceding unsigned comment added by Lrazevedo ( talk • contribs) 15:04, 24 June 2020 (UTC)
References
I added a pedagogical introduction at v:Divergence theorem. As per regs, the link is situated at the bottom under "External links". The editors of this article can choose to mention and/or link to v:Divergence theorem in the lede or elsewhere else. If there is anything in the Wikipedia article you would like to have sent to Wikiversity, leave a note at v:User talk:Guy vandegrift and I will help you. At Wikiversity we use lots of subpages, giving us more freedom to add material that might not interest all readers.-- Guy vandegrift ( talk) 03:43, 19 March 2021 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
(Moved from my talk page)
Thank you for your changes to divergence theorem. However, I have some remarks about links.
First, one should not link to plural, rather to singular, so it's got to be [[divergence]]s and not [[divergences]]. Second, you should wonder if links are actually needed, a link to sink does not make any sence in that article.
Third, one should check where the links point to. Instead of boundary one should link to [[boundary (topology)|boundary]]. Fourth, a link to " conservation law" should be instead conservation law, because, as you notice, those two words go together.
These are minor things, but it helps give value to the links. Thanks. Oleg Alexandrov ( talk) 10:38, 29 October 2005 (UTC)
By symmetry,
Why? -- Abdull 19:30, 2 June 2006 (UTC)
I have added a bit of clarification to the section for spherical symmetry. I was prompted by a change provided by 83.30.188.66 ( talk · contribs), which was aiming for clarity, but technically introduced an error. I hope the rewording I have now supplied makes it a bit clearer. Further suggestions very welcome. — Duae Quartunciae ( talk · cont) 11:48, 5 August 2007 (UTC)
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:48, 10 November 2007 (UTC)
Could somebody with the requisite mathematical expertise please fill this in?
I made dedicated articles for Gauss's law for magnetism and Gauss's law for gravity, and accordingly moved some material from here to those pages. (I went through and updated the links for hopefully all of the other wikipedia articles citing this material.) By the way, anyone interested in contributing to those articles is encouraged to do so. :-) -- Steve ( talk) 21:08, 1 April 2008 (UTC)
On the plus side, it helps people who only know a little calculus, and aren't familiar with the idea of one squiggly-integral sign denoting anything other than a one-dimensional integral. On the minus side, it makes equations harder to read and generally more cluttered. On the plus side, anyone who can understand it with one integral sign can understand it with three, but not necessarily vice-versa. On the minus side, I don't think any professional mathematician or physicist would write it this way (except maybe when they're writing introductory textbooks), and at least the physics articles I've seen on Wikipedia don't write it that way either.
Has anyone thought about this issue, pro and/or con? I have mixed feelings, myself. -- Steve ( talk) 21:07, 8 April 2008 (UTC)
I once (far far time ago) learned about other (of the many, Wikipedia should have a disambiguation page or something about this, its a serious issue) algorithm called "Gauss theorem", used for findings roots equations (of any power) when [independent coefficient]/[primary coefficient] is an integer by "trying" with different roots gotten by finding divisors of that division. How is this theorem called in Wikipedia-Other parts of the world other than my classroom? -- Me ( talk) 23:34, 19 September 2008 (UTC)
The condition of the div theorem says that F must be C1. How can the theorem be applied then for example, for , where G is a Green's function? Typically, Green's functions have a singularity, so they are not C1. Does this mean the divergence theorem can be extended? -- Janzz2k 17:21, 19 April 2007 (UTC)
The condition of the div theorem states that F must be C1. However, the derivative does not need to be continuous. This can be proven by decomposing the volumetric domain into subregions where the function is C1. It is readily seen that if the function is continuous, the terms corresponding to interior boundaries will cancel. —Preceding unsigned comment added by 128.115.27.10 ( talk) 17:22, 16 March 2011 (UTC)
Anyone interested to add something about application of Gauss's law in acoustics published in http://www.arxiv.com/abs/1104.0893 — Preceding unsigned comment added by 93.139.121.178 ( talk) 19:08, 30 May 2011 (UTC)
In my calculus book I remember that Green's theorem could be obtaneid as a particular case of Gauss theorem. I think all u had to was to remove one coordinate. — Preceding unsigned comment added by 85.18.50.180 ( talk) 11:50, 5 June 2011 (UTC)
Because this article is specifically about the divergence theorem and not about general Vector fields, I felt that the picture given in the example ( found here) had little to offer to a reader's understanding of the divergence theorem or the example. I've since rendered and inserted a replacement image with the example field plotted. Glosser.ca ( talk) 01:09, 5 November 2011 (UTC)
(Inspired by the Green Theorem comment above.)
What do people think about discussing the two-dimensional (or n-dimensional) case, instead of just 3D? I know we've decided in the past to leave all generalizations to the Stokes' theorem article, but looking at that article, it seems to me like Stokes' theorem is more abstract and more general and more complicated than just the straight generalization of the divergence theorem. In particular, non-mathematicians (e.g. engineers) may be interested in the 2D divergence theorem but would not be well served by the Stokes' theorem article. :-) -- Steve ( talk) 18:47, 5 June 2011 (UTC)
Sorry about the table in the 1st Example to complicate the markup, but the new template is gradually becoming popularized on WP, so a table was required to block the template integral expression and the lines of calculation tidily:
which translates to the mark-up: =(
:{| |- valign="top" | {{oiint | intsubscpt = <math>\scriptstyle S</math> | integrand = <math>\mathbf{F}\cdot\mathbf{n} \, dS</math> }} || || <math> \begin{align} &= \iiint\limits_W\left(\nabla\cdot\mathbf{F}\right) \, dV\\ &= 2\iiint\limits_W\left(1+y+z\right) \, dV\\ &= 2\iiint\limits_W \,dV + 2\iiint\limits_W y \,dV + 2\iiint\limits_W z \,dV. \end{align} </math> |}
F = q(E+v×B) ⇄ ∑ici 20:28, 2 April 2012 (UTC)
I've just been going over my notes from Maths, and I've noticed that the gauss integral doesn't specify a closed surface (). Can anyone confirm that it doesn't need the closed surface part? (sorry, can't figure out the double closed integral) —Preceding unsigned comment added by Jporteous ( talk • contribs) 14:33, 8 September 2008 (UTC)
Claiming it is corrected called something based on who gave the first rigorous proof is interjecting the author's opinion in how theorem's should be named. Fermat didn't prove Fermat's Last Theorem, Stokes didn't prove what we now call Stokes' Theorem in geometry, etc. If someone wants to include it being called something else that's fine, but saying one way is correct is an opinion which doesn't belong here. RyanEberhart ( talk) 19:50, 20 September 2012 (UTC)
Here is the text from the article: "Let's say I have a rigid container filled with some gas. If the gas starts to expand but the container does not expand, what has to happen? Since we assume that the container does not expand (it is rigid) but that the gas is expanding, then gas has to somehow leak out of the container. (Or I suppose the container could burst, but that counts as both gas leaking out of the container and the container expanding.)"
This is not true. If the gas expands, due to, perhaps, an increase in temperature, then the pressure in the container will rise, without the volume of the container necessarily changing. This is why things explode in the first place—the pressure builds up due to gas expansion (temperature increase) but gas cannot escape, leading to a pressure build-up and eventual explosion. I don't know enough math to suggest a better example, but this one is severely flawed.
24.60.252.143 ( talk) 15:57, 13 August 2014 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Divergence theorem. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
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(last update: 18 January 2022).
Cheers.— InternetArchiveBot ( Report bug) 03:30, 14 December 2016 (UTC)
I'm not an expert on the topic, but could the article be improved by adding a proof? 50.39.171.4 ( talk) 19:33, 1 November 2018 (UTC)
In both given examples, you are using and . Since we are not used to it: Is this a standard notation for the unit vectors? — Preceding unsigned comment added by 129.27.232.39 ( talk) 10:28, 9 December 2018 (UTC)
I haven't been able to find a proof or reference for the divergence theorem for surfaces with piecewise smooth boundary. The reference provided does not mention boundary smoothness at all, nor does it provide any proof or references. Does anyone know of a proof in the piecewise smooth case, and if so can they add it? — Preceding unsigned comment added by 129.94.177.30 ( talk) 05:34, 7 January 2020 (UTC)
A statement and proof of the piecewise-smooth case in three dimensions can be found in this book. [1] Does this require a proof for an arbitrary number of dimensions? Or would this reference suffice? Benjamin Schulz ( talk) 23:12, 4 April 2020 (UTC)
The book "Calculus on manifolds - Spivak - 1968", on page 137, says the theorem is true for piecewise-smooth case. — Preceding unsigned comment added by Lrazevedo ( talk • contribs) 15:04, 24 June 2020 (UTC)
References
I added a pedagogical introduction at v:Divergence theorem. As per regs, the link is situated at the bottom under "External links". The editors of this article can choose to mention and/or link to v:Divergence theorem in the lede or elsewhere else. If there is anything in the Wikipedia article you would like to have sent to Wikiversity, leave a note at v:User talk:Guy vandegrift and I will help you. At Wikiversity we use lots of subpages, giving us more freedom to add material that might not interest all readers.-- Guy vandegrift ( talk) 03:43, 19 March 2021 (UTC)