Talk:Vector calculus identities

message: Hello. I wonder if anyone is opposed to rewriting the identities as curl grad foo = 0, etc, i.e., using the words curl, div, and grad. As Wikipedia is a reference work, it seems safe to assume that we are going to get many readers who are capable of understanding the identities, but are only occasional users of the notation. Yes, no, maybe? Keep up the good work, 64.48.158.121 03:59, 19 May 2006 (UTC)
thread_title:  Restate identities using div, grad, curl (names) ? 

message: Another thing to think about -- it would be a good idea to look at the other pages in :Category:Vector calculus and see if there are some identities which can be copied here. 64.48.158.121 04:01, 19 May 2006 (UTC)
thread_title:  Collect identities from other pages here 

message: I think it would be good to mention how Cartesian tensors in rectangular coordinates (a condition which I didn't state in a previous edit) can be used to derive the vector calculus identities stated in this article. This method is much easier and more elegant than laboriously expanding curls of curls etc. and then grouping terms. However, detailing how this is done might expand the article a substantial amount. Any thoughts?  —Preceding unsigned comment added by Breeet (talk • contribs) 07:25, 5 May 2010 (UTC)
thread_title:  Using Cartesian tensors to derive identities 

message: Hello ... I have extended this article by adding a few more identities. Now, I think this article is superset of the other article!. So, I would like to suggest to delete(or something equivalent) the article "List of vector identities". If anybody has objection, please let us discuss. zinka 09:30, 5 May 2010 (UTC)
thread_title:   Merging with [[List of vector identities]] 

message: The present article Vector calculus identities describes identities involving integration and derivative operations like the curl and gradient. The article Vector algebra relations involves only algebraic relations like the dot and cross products, and no calculus. Inasmuch as the subsection of Vector calculus identities titled "Addition and Multiplication" does not involve any calculus (and so is not properly part of the subject of Vector calculus identities), and inasmuch as the material of this section is contained (and expanded upon) in Vector algebra relations, I have removed this section and replaced it with a link to Vector algebra relations. Brews ohare (talk) 15:18, 14 September 2010 (UTC)
replies: text: As seen in the section immediately above this one this article is the result of a merge, between Vector calculus identities and List of vector identities, i.e. it contains both vector calculus and more general identities. This makes sense as the the calculus and non-calculus identities are closely related, while the article with both of them in is not by any measure too long. There is no need now to split off this content into a separate article, undoing an uncontentious merge, forcing readers to search though two articles for closely related identities.--JohnBlackburnewordsdeeds 15:38, 14 September 2010 (UTC)
replies: text: The two different types of identity are not closely related. Repeating the non-calculus related identities here is unnecessary. Moreover, the purely algebraic identities here are only a subset of the useful identities reported at Vector algebra relations, so the reader will possibly have to go to Vector algebra relations even with this repetition. It makes no sense to duplicate. Brews ohare (talk) 16:28, 14 September 2010 (UTC)
replies: text: Ok, but eight years on and it doesn't look like anything has been done to correct it. Alternatively, should we just merge them together? --Ipatrol (talk) 20:41, 3 December 2018 (UTC)
thread_title:  Removal of overlap with [[Vector algebra relations]] 

message: I deleted the useless template + section in this edit , is it really that necessary to expand on this? An integral is an integral, if there really are widespread wacky notations in use just add as and when, instead of leaving it empty...--  F = q(E + v × B) 00:05, 2 March 2012 (UTC)
thread_title: deleted section

message: The identities curl(grad(f)) = 0 and div(curl(F)) = 0 need conditions on the scalar field f and the vector field F, namely continuous second partials in a connected open set.  This article says that the identities hold unconditionally.  — Preceding unsigned comment added by 69.210.137.176 (talk) 05:06, 11 March 2012 (UTC)
thread_title:  Conditions on second partial derivatives needed 

message: I have never seen Feynman subscript notation before. In this article it is introduced as if it is just a convenient abbreviation for a two-term operation in vector calculus, but then it is used only once! Perhaps I am dense but it just seems unintuitive, and it sticks out like a sore thumb in an otherwise beautifully concise page of identities written using the standard nabla notation. The introduction of Hestenes overdot notation is even more strange as it is not used at all.
To be clear I'm not saying alternative notations/operators don't belong on wikipedia, just that they don't fit in here. It would be nice to see an article about these, as I think there are probably many many more variants worth mentioning as long as the intuition and the gain is made obvious. --Nanite (talk) 10:48, 24 November 2015 (UTC)
thread_title:  Removal of Feynman subscript notation 

message: I know there are a few vector calculus identities involving dyadics, i.e.
\nabla \cdot \mathbf{AB} = (\nabla \cdot \mathbf{A})\mathbf{B} + (\mathbf{A}\cdot \nabla)\mathbf{B}, but I'm not sure if they should be included in this page or the dyadics wikipedia page. Thoughts?
76.116.117.40 (talk) 00:48, 22 February 2016 (UTC)
thread_title:  Dyadic calculus identites 

message: The section on the Gradient refers to "a tensor field of order n" although the meaning of "order n" for a tensor field is not explained in this article and is not explained in the linked article Tensor field, either. 
The section discusses the case of a space of dimension 3 but then suddenly starts talking about tensor fields of order n. Why?2600:1700:E1C0:F340:ED8B:9E01:6222:F4CC (talk) 19:48, 20 January 2019 (UTC)
thread_title:  Gradient section needs work! 

message: Has anyone else noticed the strange and inconsistent LaTeX spacing used for some of the identities? For example, the use of (\nabla {\cdot} \psi), written (\nabla {\cdot} \psi), in the operator notation section's special notation subsection compared to the use of (\nabla\cdot\psi), written (\nabla \cdot \psi), in the summary section's second derivative subsection. Is there a reason for this? CoronalMassAffection (talk) 03:02, 10 June 2021 (UTC)
thread_title: Inconsistent formula spacing

message: This wikipedia entry is absurdly distant from Plain English. There are dozens of articles that explain this subject so that non-experts can understand this topic. DDilworth (talk) 16:33, 27 May 2024 (UTC)
thread_title:  Plain English Introduction Needed