Talk:Differential (infinitesimal)

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Mathematics rating:	Start Class	Mid Priority	Field: Analysis
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. This can potentially fill in many gaps in other articles and should be improved in that light. Geometry guy 22:58, 29 March 2007 (UTC)

[edit] Question

Is this page about derivative or diferential? I don't see any diferentials??? Stijak 12:05, 18 September 2006 (UTC)

[edit] Definitions

at the top of this article, it says that a differential is infinitely small, without defining what `infinitely small' means. Later on, the definition from Apostal states that a differential is a real variable; in fact, the `t' in the definition of the differential is the differential itself. Hence the differential can be any real number; it doesn't have to be small.

It's not particularly useful if it's not small, but it's not required to be small.

[edit] Differential calculus vs Differential (calculus)

This page is linked from Calculus as 'Differential Calculus' so we expect a succinct exposition of same, not an explanation of the historically important but fairly minor term 'differential' in calculus. I think the whole page needs a rewrite, making use of some of the good existing material. I am considering this. Expitheta 20:33, 7 January 2007 (UTC)

For the time being, I've relinked Differential calculus to Derivative, which is a much more complete article. However, a separate article on differentiation and differential calculus would still be very welcome. As you rightly point out, this is not it! Geometry guy 11:06, 22 February 2007 (UTC)

[edit] What is this article about?

I've tagged this article for a clean-up or rewrite. It jumps so much from one vague idea to another that it is not even clear what it is supposed to be about. I think there is some scope to turn this into an article about differentials like dx and their role in:

• the traditional approach to calculus via infinitesimally small quantities
• the history of calculus
• notation such as dy/dx, and
• motivating contemporary ideas to make all this rigorous, such as

• the differential as a linear map and differential 1-forms
• approaches in algebraic and differential geometry using ringed spaces such as schemes
• nonstandard analysis and invertible infinitesimals
• smooth infinitesimal analysis, synthetic differential geometry and nilpotent infinitesimals

I don't think any of these need to be discussed in detail, as they all have their own articles, but they could be tied together here.

Comments? Geometry guy 23:55, 21 February 2007 (UTC)

Looks excellent (though I don't really have the knowledge to comment on the last point). I was pleasantly surprised with our article on infinitesimals, so it might not be too hard to pull it off. -- Jitse Niesen (talk) 01:50, 25 February 2007 (UTC)

Okay, I've started. More to follow... Geometry guy 21:27, 25 February 2007 (UTC)

I've now sketched out this approach. I'll leave the clean-up tag in place for a while to encourage other people to clarify, expand and correct what I have done. Geometry guy 19:46, 28 February 2007 (UTC)

[edit] d versus d

Any special reason why "d" for differential is not italized anywhere in this article? iNic 00:31, 22 March 2007 (UTC)

That's quite common, though probably not as common as italics. See Wikipedia talk:WikiProject Mathematics/Archive 4#straight or italic d? and other discussions throughout Wikipedia. -- Jitse Niesen (talk) 04:03, 22 March 2007 (UTC)

Aha, wow! Didn't know it was an UK/US-thing. (I can't remind myself of ever seeing the plain text d anywhere in math literature, but probably I have.) Thanks! iNic 05:02, 22 March 2007 (UTC)