Talk:Boundary value problem

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Should this redirect to boundary condition, or perhaps vice versa? Michael Hardy 20:59, 20 Jan 2004 (UTC)

Something else: this is quite a lot of text for a stub, or is it just me? Eef (A) 20:40, 14 Dec 2004 (UTC)

[edit] Examples

I think the worked examples are overkill. This page should be brief, and the worked examples moved to more specific topics (Strurm-Liouville problem or elliptic eigenvalue problems as the case may be). Brian Tvedt 14:11, 14 August 2005 (UTC)

Hi Brian, welcome here. Why do you say that this page should be brief? It seems quite a good idea to list some examples. However, the current examples are probably not the best illustration, because they are eigenvalue problems which complicates matters. I think it's better to drop the parameter λ. By the way, have you already come across Wikipedia:WikiProject Mathematics? I hope that you decide to stay around and improve some of our articles. Cheers, Jitse Niesen (talk) 15:14, 14 August 2005 (UTC)

I very much agree with Jitse. Brian, of the bad things about the math articles on Wikipedia is that sometimes they tend to be written by mathematicians for mathematicians who already know the thing. As such, a lot of math articles are completely incomprehensible to nonmathematicians.

According to the math style manual, at least the introduction of an article should be at the level of high school students. Thus, examples are definitely helpful. A dry definition willl not help anybody learn. Oleg Alexandrov 15:37, 14 August 2005 (UTC)

Oleg, I'm certainly not saying the article should be overly technical--quite the contrary! I think it would be improved by more emphasis on high-level description, rather than grinding through separation of variables. I added an (overly simplistic) paragraph on the notion of well-posedness as a nudge in this direction.

To answer Jitse's question, part of my thinking was that we already have a subtopic in the PDE article on specific methods of solution, and that would be a better place to collect worked examples. I'm certainly not opposed to examples in principle. (BTW, the kind welcome is appreciated.) (unsigned post by Brian Tvedt)

I see your point. Your high-level description coupled with my simple example (without separation of variables) might as well make people understand what is going on. I still like the PDE example though, even if it is technical. It is the last example, so it can be complicated, and it gives a good idea of where boundary value problems are used. Oleg Alexandrov 00:35, 16 August 2005 (UTC)

[edit] as a non mathematician...

I can't get a mastery of the subject, but I wonder, is it possible that it bears on the problem of the 'joints' as mentioned by Socrates in the Symposium? That is, our senses allow us to perceive certain kinds of boundries intuitively but how do we decide where the joints lie otherwise. I know this is a very long shot ( in the dark ) but perhaps someone will help me find a matchup somewhere in maths. wblakesx~~

I'm not familiar with the passage, and don't have Plato handy, but it is conceivable that Socrates was fumbling towards a concept related in a crude way to the modern mathematical notion of 'boundary value problem'. Such a connection would be fascinating, but if you find it, keep in mind this counts as original reseach, so Wikipedia is not the place to publish it. Brian Tvedt 12:50, 22 December 2005 (UTC)

[edit] Other types of boundary value problems

There are many boundary value problems studied by mathematicians (mostly complex analysts and potential theorists) which do not fall under the heading of solutions of differential equations. For example, there is a lot of research into the boundary behaviour of (discontinuous) subharmonic functions, meromorphic functions, fine-continuous functions, etc. etc. I feel tempted (when I get some time) to write something about these problems somewhere, but the question is: do they belong here, or in a separate article, and if so, then what should it be titled? Madmath789 09:10, 1 August 2006 (UTC)

I would suggest to start a section here and if it is too big create a separate article. Rex the first ^{talk | contribs} 23:00, 1 August 2006 (UTC)