Talk:Divergence

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Start Class Mid Priority  Field: Analysis
One of the 500 most frequently viewed mathematics articles.
WikiProject Physics This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.
Start This article has been rated as Start-Class on the assessment scale.
??? This article has not yet received an importance rating within physics.

Help with this template

Comments:
WikiProject Meteorology
 This article related to meteorology and/or specific weather events is part of WikiProject Meteorology and Weather Events, an attempt to standardize and improve all articles related to weather or meteorology. You can help! Visit the project page or discuss an article at its talk page.
Start This article has been rated as Start-Class on the assessment scale.

Contents

[edit] Non-general definition

The definition of divergence, it seems to me, should be defined for any amount of variables. Am I wrong in this, or can a four variable function have a divergence as well? Fresheneesz 20:48, 10 February 2006 (UTC)

The divergence is of course defined in any dimension. But it makes most sense in 3D only, as ther it behaves nicely with the curl, and has a physical interpretation. I will now add a mention of the general case. I would be opposed to rewriting this article from the n-dimenional perspective, as a lot of the physics would be lost, I think. Oleg Alexandrov (talk) 02:59, 11 February 2006 (UTC)

[edit] Initial example

The example of water in a bathtub can be confusing. Water does not 'vanish', and the divergence of water flow is in fact very close to zero. I've changed this to air expanding which is a better example. PCM —This unsigned comment is by Paul Matthews (talk • contribs) .

On further reflection, I think you are right. Oleg Alexandrov (talk) 02:09, 15 March 2006 (UTC)

actually i want to ask that if ▼.B is equal to B.▼.... if it is i just cant understand its physical interpretation..as ▼.B means a operator is operating over B but what then B.▼ implies?? 210.212.8.61 17:18, 6 February 2007 (UTC)

[edit] definition

I think definition should be as general as possible. therefore,

\nabla\cdot\mathbf{F}=\lim_{V\rightarrow 0} \frac{\oint_{s}\mathbf{F}d\mathbf{s}}{V}

Eventually, in 3D orthogonal system, this expression becomes the known one.

Nevo taaseh 11:32, 8 April 2007 (UTC)

I think it is preferrable that definitions start simple, not general. Things can be generalized later I believe, once the basic concept is clear. No? :) Oleg Alexandrov (talk) 15:06, 8 April 2007 (UTC)

[edit] Abuse of notation

Is ∇·F actually an abuse of notation? ∇ is a vector and can operate on scalar or vector quantities. If it operates on a vector, then one needs to know if it performs a scalar product or a cross product, see curl (∇xF).

I agree that it is not an abuse of notation. ALittleSlow 02:02, 30 September 2007 (UTC)

[edit] Visualisation

This article could do with a nice visualization as in the gradient article —Preceding unsigned comment added by 137.205.125.78 (talk) 09:47, 26 October 2007 (UTC) sad —Preceding unsigned comment added by 207.148.171.2 (talk) 22:15, 7 April 2008 (UTC)

[edit] WikiProject class rating

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)


[edit] More definition concerns

From the definition section:

Let x, y, z be a system of Cartesian coordinates..

AFAIK the divergence operator can be defined in other coordinates, right?Mathchem271828 (talk) 06:59, 1 June 2008 (UTC)