Talk:Ordinary differential equation
The first paragraph is not quite technically correct. It's not a bad start, but should be refined a bit.
If you could elaborate in its technical incorrectness, I'll get refining... GWO
Now you have something to pull apart...RoseParks
Just a typesetting note: when doing some minor copyediting here, I discovered that using an ordinary apostrope (') for the "prime" sign really wreaks havoc on the Wiki software (especially when doubled), since it tries to interpret them as bold, italics, etc. The "correct" thing to do would be to use ′, but some browsers won't handle that well, and there's no other tricky notation on this page to justify the use of special characters. So I have used the bare-acute-accent character ´ (decimal 0180) for the prime symbol. It should work on all browsers using either ISO or Windows ANSI, and doesn't screw up the Wiki software. --LDC
Superb!
Now for the nits... (heh) For an ODE, we really speak of a function x of a single parameter t, that is, x = x(t)...
The really frustrating thing about math is that so much of the notation I learned in lower division I more or less had to unlearn in upper division or grad level classes.
Perhaps some mention of the different types of differential equations and methods for solving them would be appropriate (i.e. linear first and second order, etc.) --BlackGriffen
No talk at all about the relationship to Vector fields, which are really ODEs wearing funny hats, except they exist on differential manifolds and can be defined without co-ordinates.
- Would you like to add a paragraph about that connection? AxelBoldt
Is there any reason why this article uses the plural title?
- nope. should be fixed. AxelBoldt
- yep. "Differential Equations" is the name of a field of study in math. A "differential equation" (singular) would be the object of that field of study. I will move the article to the singular, leaving a link from the plural. Ed Poor
I believe that the history section here ought to be rewritten preferrably by someone who knows something about it and doesn't simply 'copy' a 100+ year old book on the subject - and doesn't tell that's what have been done! I see that there are a number of references to 'recent works', 'the modern school' and so on, when referring to texts written well over a century ago! 'Recent writers' refer to (amongst others) Klein (-1925), Weierstrass (-1897) and Frobenius (1849-1917). Do you agree that the history part here should be deleted? Mikez 18:00, 23 Feb 2004 (UTC)
Please don't delete. Quite a bit of work has been done already - obviously it is still in a bad state, but starting again with nothing isn't a good idea. In the end there will have to be major changes - of course.
Charles Matthews 18:13, 23 Feb 2004 (UTC)
This now removed - hard to upgrade:
The modern school has also turned its attention to the theory of differential invariants, one of fundamental importance and one which Lie has made prominent. With this theory are associated the names of Cayley, Cockle, Sylvester, Forsyth, Laguerre, and Halphen. Recent writers have shown the same tendency noticeable in the work of Monge and Cauchy, the tendency to separate into two schools, the one inclining to use the geometric diagram, and represented by Schwarz, Klein, and Goursat, the other adhering to pure analysis, of which Weierstrass, Fuchs, and Frobenius are types. The work of Fuchs and the theory of elementary divisors have formed the basis of a late work by Sauvage (1895). Poincar\'e's recent contributions are also very notable. His theory of Fuchsian equations (also investigated by Klein) is connected with the general theory. He has also brought the whole subject into close relations with the theory of functions. Appell has recently contributed to the theory of linear differential equations transformable into themselves by change of the function and the variable. Helge von Koch has written on infinite determinants and linear differential equations. Picard has undertaken the generalization of the work of Fuchs and Poincar\'e in the case of differential equations of the second order. Fabry (1885) has generalized the normal integrals of Thomé, integrals which Poincar\'e has called "intégrales anormales," and which Picard has recently studied. Riquier treated the question of the existence of integrals in any differential system and gave a brief summary of the history to 1895. The later contributors include Brioschi, Königsberger, Peano, Graf, Hamburger, Graindorge, Schläfli, Glaisher, Lommel, Gilbert, Fabry, Craig, and Autonne.
Charles Matthews 11:52, 12 Apr 2004 (UTC)
Ok...Mikez
L-H revert
Unfortunately, I can't make sense out of the sentence "Differential equation was born as the fundamental equation which describes the natural law." It contains grammatical errors which could be fixed, but the meaning is still too unclear to me. So I reverted. I notice that the sentence in question links to fundamental equation. I question whether this usage is standard.
Seems like a lot of the history on this page may be a copyvio? We definitely at least need the source of all this stuff. I'm working on it to make sure the dead men don't seem to be alive :-) - Gauge 21:18, 4 Aug 2004 (UTC)
No, from an old PD source I believe: User:Recentchanges added this and similar stuff on a number of pages. Charles Matthews 06:15, 23 Aug 2004 (UTC)
How much schooling do I have to go through in order to be able to understand ANY of this? I am just curious: what is the education level of the authors of this page?