The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was Keep (non-admin closure), per wp:snow Oo7565 (talk) 23:29, 22 July 2008 (UTC)"[reply]

Change of variables (PDE)

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Contested prod. How-to guide, one of the things Wikipedia is not. Septentrionalis PMAnderson 20:32, 18 July 2008 (UTC)[reply]

Keep. The article has been criticized by Ryan Reich based on my motivations for creating the article, as much as for the quality of the article. I don't think motivations for creating an article are a valid basis for criticism; the article itself should be discussed on its own terms. (See the article Talk Page for the thread.) His criticisms of the article can be seen as a guide for improvement, not as a reason for deletion. This article documents a technique basic to symbolic computation with PDEs. It is no more or less relevant than the article on Integration by substitution. It's something that exists, is significant, and is worthy of note. If someone has a problem with the quality of the writing, then that person should feel free to improve the exposition and add what they think to be the relevant information for people who are interested in this topic. What is obvious to one person may not be obvious to another. I know, after doing a lot of Internet searches on this topic, that there is not a clear, simple, short and definitive exposition on this topic, but it is used in a casual way in many applied math expositions involving PDEs. That is actually a tricky issue is documented by a quotation from a Wikipedia-listed mathematician which is in the article. Ryan Reich could improve the article, following his criticisms, by:

Providing a better exposition of the general principle
Saying in a better way what the technique accomplishes
Giving a better example which illustrates the technique

Thanks, Erxnmedia (talk) 22:14, 18 July 2008 (UTC)[reply]

Delete. See the discussion on the talk page for my response to the claim that I'm basing my criticisms on an assessment of Erxnmedia's motivations. I have also written there why I think this article is necessarily a how-to guide, and I believe that Erxnmedia's statement above affirms that he wrote the article as such a guide and would expand it to include more material in this vein (this is the short version of why his motivations are relevant, if not central to my criticism of the article). In particular, this article is much less relevant in its area than integration by substitution is in its, essentially because integration by substitution is an idea which goes above and beyond either its applications to symbolic integration or its connection to the chain rule, whereas substitution in differential equations is firmly a subset of both symbolic manipuation and the chain rule. It is not necessarily the role of Wikipedia to inform professionals in the use of a technique which is part of their work; occasionally, particularly in math, it functions that way because the tools of the trade are also part of the trade. Nonetheless, one could write an article on blacksmithing without being at all useful to blacksmiths, even in those issues which are tricky and badly-documented on the Internet. And not every mathematical tool is an object of independent study in math, particularly (as in this case) when it is an instance of something larger and more significant which has been specialized to a context in which nothing detailed can be said about it. I don't think this article can be rewritten to avoid being redundant with a discussion of the chain rule and also to avoid excessively instructing merely the technique of substitution. Ryan Reich (talk) 02:57, 19 July 2008 (UTC)[reply]

Note: Wikipedia is not a professional mathematical journal, and there is no reason to limit information about mathematics in Wikipedia solely to information which is of interest only to professional mathematicians specializing in that aspect of mathematics. Like it or not, change of variables in PDE is hard to do. The quote from J. Michael Steele in the current article was from a book on stochastic processes, not PDEs. There are many people who need to apply mathematics in professions other than mathematics, who need some correct information about a particular corner of mathematics which is accessibly presented, not like a JAMS submission in which all which would be apparent to an expert in the topic is ellided. Erxnmedia (talk) 13:16, 19 July 2008 (UTC)[reply]

Keep Looking on this as an how-to guide seems a drastic extension of the meaning. Seen in this light, most mathematical topics could be seen as how to prove something or other. Not the most sophisticated mathematical article in Wikipedia, but elementary levels are acceptable too. DGG (talk) 07:14, 19 July 2008 (UTC)[reply]
Keep per DGG. --Itub (talk) 07:34, 19 July 2008 (UTC)[reply]
Weak keep - Appears to need large portions substantially rewritten to become truly encyclopedic, but I'm wary to delete anything so comprehensive. Per DGG it seems reasonable for a mathematics article that clearly needs some cleanup work. -FrankTobia (talk) 07:52, 19 July 2008 (UTC)[reply]
Keep for improvement, any first DiffEq textbook will attest to the significance of the subject. WillOakland (talk) 18:37, 19 July 2008 (UTC)[reply]
Keep. I know pedagogical arguments do not really hold sway in these discussions, but there are some truly fascinating bits of functional theory behind the ~~how-to~~ [edit: current theory-sparse article]. In any case, the technique is treated by any Differential Equations book (perhaps a more standard mathematics text should be cited in addition to the Financial Applications?) sufficiently to be covered by the encyclopedic mandate - Eldereft (cont.) 08:47, 21 July 2008 (UTC)[reply]

Hi Eldereft, Can you add the functional theory to the article? I stated the general technique as best I could, but I am not an authority, and I am looking forward to someone with more experience and training supplying a deeper explanation of the theory behind the technique. Roughly speaking, I would guess that every change of variables can be cast as a coordinate system transformation, so the theory of coordinate system transformation would apply in this case. Also, the financial application (Black Scholes), which involves multiple change of variables, doesn't make clear the connection with coordinate system transformation. (It kind of looks more like a card trick -- it shows what can be done, but it doesn't necessarily make clear what's behind the curtain.) Thanks, Erxnmedia (talk) 15:14, 22 July 2008 (UTC)[reply]

Keep This is an important technique and not a How-to guide. QuantumShadow (talk) 11:55, 22 July 2008 (UTC) "[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.