Talk:Differential (infinitesimal)

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Mathematics grading:	Start Class	Mid Importance	Field: Analysis
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)

Contents 1 Question 2 Definitions 3 Differential calculus vs Differential (calculus) 4 What is this article about? 5 d versus d

[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)