Timeline for Simplest proof of dimension of solution space for linear ODEs [closed]
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| May 25, 2011 at 12:32 | comment | added | Michael Bächtold | Maybe asking the same question but about the dimension of the solution space of nonlinear ODE's would make it more acceptable? | |
| Nov 8, 2010 at 5:50 | comment | added | Zen Harper | Are you saying that a question has to be both difficult and highly interesting for it not to be closed? If you don't know the answer, how can you be sure of either of those things, let alone both? I didn't think about this for very long, and I'm annoyed with myself for not seeing the answer, but that's precisely why we shouldn't judge serious questions too harshly. Anyway, a large amount of research started from teaching, so it shouldn't be dismissed so quickly. I agree that this question has a fairly low order of nontriviality, but not sufficient to justify closure in my opinion. | |
| Nov 8, 2010 at 5:44 | comment | added | Zen Harper | OK, so it's not really so difficult, as Andrey's comments make clear; but it's not a stupid question, and it's not trivial, and it's not the crazed ravings of a demented nutter, and it's of interest to mathematicians (to me, anyway). And maybe there is another nice direct proof for this special case, which could be interesting. Remember that we don't have uniqueness even for very simple nonlinear equations, so it's conceivable that maybe a new direct proof could be generalised to certain types of nonlinear equations. | |
| Nov 5, 2010 at 11:52 | comment | added | Thierry Zell | I agree with closure: if anon and Zen make decent arguments that the answer may be interesting, it's only truly the case if the question is carefully formulated to make it compelling. There may be something to say from the teaching angle, but that's not what is being asked, and anyway the status of questions about teaching on MO is unclear at best. | |
| Nov 5, 2010 at 9:16 | comment | added | Andrey Rekalo | I think this result is proved in most undergraduate books on ODEs. Existence and uniqueness of a solution to an initial value problem for the ODE follows e.g. from the general Picard–Lindelöf theorem. And the Liouville formula implies that there are exactly $n$ linearly independent solutions (which correspond to any $n$ linearly independent initial data points). | |
| Nov 5, 2010 at 6:01 | comment | added | Zen Harper | I agree with anon - I also don't think this deserves to be closed; it is a natural and important question, and well written. Call me stupid if you like, but it doesn't look obvious or trivial to me; in fact I don't even know any answer, I need to think about it. Note that ahh doesn't assume constant coefficients (and even that case is not completely trivial, needing exponentials of matrices and Jordan normal forms or similar). | |
| Nov 5, 2010 at 5:19 | comment | added | anon | I don't understand why this was closed. I'd bet if someone asked for the easiest proof of some standard result in another subject (e.g. Bezout's theorem for plane algebraic curves), there would be a host of responses. Mathematicians do interest themselves in questions like these, especially when teaching. I can't help but suspect that because the subject matter is differential equations, and not something nearer and dearer to the community's heart, the benefit of the doubt is not being given, and it is being assumed that this is some kind of homework thing and not a valid question. | |
| Nov 5, 2010 at 2:39 | history | closed |
Andrey Rekalo Will Jagy Deane Yang Qiaochu Yuan Andrés E. Caicedo |
too localized | |
| Nov 5, 2010 at 2:35 | answer | added | anon | timeline score: 8 | |
| Nov 4, 2010 at 19:26 | comment | added | Qiaochu Yuan | This is not really appropriate for MO. You might have better luck with this question at math.stackexchange.com. | |
| Nov 4, 2010 at 18:15 | answer | added | Pietro Majer | timeline score: 5 | |
| Nov 4, 2010 at 18:04 | history | asked | ahh | CC BY-SA 2.5 |