Talk:Laplace's equation

Hmmm. You're right, CSGuy. That's appalling, especially for something written by 3 mathematically literate people: Andy, Roger, and Jaques. (Who's Jaques? Look around. Not active any more, but was a very prolific and erudite contributor in science and math.)

Let me think about this. I'll fix it tomorrow. SamHB 19:18, 28 April 2008 (EDT)

How to proceed

I'd like to update this with some material along the lines of

Laplace's equation is the statement that the Laplacian of a function is zero. In the simplest case, this is a real-valued function of 2 or 3 (or more) variables. More generally, it is a scalar field (or even an arbitrary tensor field) on a Riemannian manifold.

and then go in one or the other (or both) of two directions:

• What that means in terms of partial derivatives, that is, partial^2 psi/partial x^2 + partial^2 psi/partial y^2 = 0, and so on. This seems to be what the original authors of the page were getting at with the reference to "non-mixed partial derivatives".
• Go into the physics of it instead, about what it means -- heat flow, complex analytic functions, the wave equation, etc.

I'm concerned about what the right thing is for an educational encyclopedia for high-shool-age students. This is what I think Conservapedia is for, and I don't want to lose sight of that. So a whole lot of partial differential equation theory is probably not right, but we could point out that, because of Laplace's equation, we know how to find the equilibrium temperature of a heat-conducting membrane with arbitrary temperatures imposed at the boundary. This is a problem that high-school-age students can appreciate, even though it is probably far beyond their ability to solve. We want to tell them that there are known mathematical techniques that can solve that problem.

But there are larger problems with this, including the whole issue of math/science articles on Conservapedia, and the issue of whether discussion of complex analytic functions is frowned upon here. I have put that discussion on my user page User:SamHB, because it really isn't specific to the Laplace equation page. I'd like to know what people think before going ahead with anything.

SamHB 20:02, 2 May 2008 (EDT)