User talk:Donludwig

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[edit] Welcome

Thank you very much for your contribution to our article on partial differential equations. That article is in a pretty sorry state and it is great to see somebody working on it. I am wondering though whether the parts you added might not be better placed at our articles on the heat equation and the wave equation. As I'm sure you know, there is a lot to be told on PDEs, so we have to be careful what to put in partial differential equation. For the moment, it's not much of a problem, but it might be good to keep this in mind if (as I hope) you intend to expand the PDE article further.

You seem to have found out the essential information on how Wikipedia works. In case you haven't found it, you might also be interested in Wikipedia:WikiProject Mathematics. The associated talk page is a good place if you have a maths question related to Wikipedia, and you can also look at the list of Wikipedians editing mathematics articles and perhaps add youself. If you have any questions, please feel free to ask me on User talk:Jitse Niesen.

By the way, UBC is a very nice place to be. I was there for a conference a couple of years ago and I liked Vancouver very much.

I hope you continue contributing, and more importantly, that you enjoy Wikipedia.

Best wishes, Jitse Niesen (talk) 01:07, 2 March 2006 (UTC)

Thanks for your note about PDE. I'm new to Wiki stuff, so any help will be appreciated.

I have taken the position that the role of Wikpedia should be to supply basic information to a wide audience, such as the significance of various fields of mathematics, and supply references and guidance for further study. I especially would like to reach talented but untutored people who might then be inspired to further study.

In writing a revision of the PDE article, I wanted to illustrate the variety and depth of the field, and a sense of its wider connection to a variety of scientific problems. What I did on heat equation and wave equation is intended as a summary and perhaps a teaser to inquire further. Hence I wanted to put it up front in an introductory section.

I intend to do something similar for the 2D Laplace equation, describing its connection with complex analysis, fluid flow, electrostatic potential, etc.

As for the remainder of the main PDE article, I think it would mostly consist of references to more specialized articles, and maybe to a Wikibook on PDE. The Wikibook on ODE actually has a bit on PDE, but I think they should be separated.

I'm a student of Courant, and I helped with the English edition of Courant-Hilbert Vol II. I'd like to incorporate some of his point of view in the Wikpedia. My next project (after some preliminary work on ODE and PDE) would be Calculus of Variations, since that was Courant's favorite topic. Donludwig 20:16, 2 March 2006 (UTC)

Of course, the wave, heat and Laplace equations are prototypes for hyperbolic, parabolic and elliptic equations and I agree that they should to be treated in the main partial differential equation article. I also agree with what you wrote above, in particular that you want "to illustrate the variety and depth of the field, and a sense of its wider connection to a variety of scientific problems".

The parts that I'm not so keen on are about the algebraic manipulations, for instance, the section on separation of variables for the heat equation (I'm sorry I didn't make this clear immediately). I think the computation can be removed from the article, and that it would be better to state only the ansatz u(t,x) = T(t)X(x) and the result

The detailed computation can go in a Wikibook, or perhaps in a proof subpage as proposed on Wikipedia:WikiProject Mathematics/Proofs, or in a more specific article like seperation of variables or wave equation. Of course, this is all just my opinion. -- Jitse Niesen (talk) 01:05, 5 March 2006 (UTC)

[edit] Sandbox

Hi. You may be interested in having a personal sandbox in which to place article drafts and all other sorts of temporary things. I have taken the liberty of creating your very own sandbox and filled it with your current draft for the PDE article. If you like the idea, you can remove the draft from your user page and instead put [[User:Donludwig/Sandbox]] to link to it. I hope you find that useful, and welcome you to Wikipedia! -- Meni Rosenfeld (talk) 20:44, 2 March 2006 (UTC)

[edit] Style tip

Hi there. I see you already ran into quite a bit of mathematicians over here. :)

A style tip. On Wikipedia one should use capitals sparingly, per the manual of style. So one writes "Green's function" rather than "Green's Function", etc. Cheers, Oleg Alexandrov (talk) 03:58, 29 March 2006 (UTC)