# Talk:Laplace's equation

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Field: Analysis

## Numerical solution

This is a great article, but I think it would be great if it gave a primer on how to solve the equation numerically. Joelthelion (talk) 20:39, 19 July 2013 (UTC)

## Toroidal coordinates

hi, one question! what is laplacian equation in toroidal coordinates(r,phi,theta)? tnx alot i waite for your answers bye

${\displaystyle {1 \over r^{2}}{\partial \over \partial r}(r^{2}{\partial f \over \partial r})+{1 \over r^{2}\sin \theta }{\partial \over \partial \theta }(\sin \theta {\partial f \over \partial \theta })+{1 \over r^{2}\sin ^{2}\theta }{\partial ^{2}f \over \partial \phi ^{2}}=0}$

I just wanted to comment that this is an excellent article and, in particular, it's written very well!Andrei r 18:50, 21 February 2007 (UTC)

## Sorry for mixup

I thought someone had replaced many of the nabla symbols with delta symbols and changed everything to nablas removing the deltas.

Sorry, my mistake; I have just realized the use of a notation I was not familiar with. I apologize - have reverted the article to original state.

152.3.68.83 (talk) 21:45, 28 March 2012 (UTC)

## Physics exemple

I think the current discussion of the physics exemples could give the misleading impression that the Laplace equation only is useful in two dimensions. It is of course the case that the Laplace equation can be used in three-dimensional electrostatics and fluid flow (though my impression is that the cases in fluid mechanics where the Laplace equation can be applied are quite few) in the same way as in two dimensions. It is the connection with complex analysis that is lost. —Preceding unsigned comment added by 90.229.231.115 (talk) 19:52, 26 October 2007 (UTC)

## Fluid flow 2D example

You may want to explain why ux+vy=0 describes an incompressible fluid. —Preceding unsigned comment added by Sprevrha (talkcontribs) 19:45, 19 September 2008 (UTC)

## Excellent article

This seems to me an exceptionally clear (and concise) overview of the subject.

I don't know where the "class = B" rating comes from, but I would call this article a model of exposition.

## f vs. phi in the definition

Hi

in the defition of the Laplace- problem there is the function f used for the function phi. I know it is because of spherical coordinates with variable phi and function phi but f isn't a good coice becaus f is used in the end of that part for the right side of the poisson equation. Do someone have a solution for that? --Shinji311 (talk) 09:20, 23 September 2010 (UTC)

## Qualitative and technical description

This article currently lacks a qualitative and technical definition of the Laplace equation. See Spherical_harmonics#Laplace.27s_spherical_harmonics for a good technical wording for the definition. A qualitative definition remains to be provided and should be included at the very beginning of the article so that a non-expert reader can gain some understanding. --BBUCommander (talk) 20:45, 15 May 2013 (UTC)

## Wrong index in Curvilinear coordinates

Correct me if I'm wrong, but I believe that the second index on the metric should be ${\displaystyle i}$, not ${\displaystyle j}$, inside the derivative. I.e., the equation would read

${\displaystyle \Delta f={\frac {\partial }{\partial \xi ^{j}}}\left({\frac {\partial f}{\partial \xi ^{k}}}g^{kj}\right)+{\frac {\partial f}{\partial \xi ^{j}}}g^{jm}\Gamma _{mn}^{n}=0,}$

Currently there are two free indices, ${\displaystyle i,j}$, in the first term and none in the second term. I believe there should be no free indices since it is a scalar equation.

Mjohnrussell (talk) 14:04, 15 October 2014 (UTC)