Talk:Differential calculus

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This article could use a smoother, less-technical intro. --DanielCD 21:52, 21 October 2005 (UTC)

Contents 1 Merge 2 New version 3 Oh dear 4 WAY WAY to complicated, less meat and more show offy symbols and explinations 5 Functions that are not lines

[edit] Merge

This article used to redirect to, firstly Calculus and then Derivative, before it was started again in its present unreadable form. The section "Differential calculus" in the Calculus article, mentions main article as Derivative, which is thoroughly readable. I suggest the two articles be merged. However, I don't know which name would be better to keep - possibly "Differential calculus" seeing as this is the mathematical process? Cormaggio ^@ 14:47, 11 November 2005 (UTC)

This page is a mess, salvage what you can and mix with something else Signed_in 10:04, 18 November 2005 (GMT)

[edit] New version

As discussed on Talk:Derivative, Differential calculus is being turned into the lead article for (surprise!) Category:Differential calculus. It will not focus on the derivative operator (as the old differential calculus article did), but instead on history and applications. The present version is mostly grabbed from the present derivative article, plus some additions (mostly the sketch of the derivative operator). 141.211.62.20 03:28, 28 July 2007 (UTC)

[edit] Oh dear

This has a textbook tone! Needs to be fixed :) Uxorion 23:11, 10 August 2007 (UTC)

Go for it.  :-) 141.211.120.81 23:41, 10 August 2007 (UTC)

[edit] WAY WAY to complicated, less meat and more show offy symbols and explinations

Shall i ad a parra on the rules in differentiation. Eg product rule, quotient rule, chain rule etc as well as differentiation of trignometric values? the article basically talks about the history of differentaition-(yawn) and also how y' (y dash) can be written differently. WHERE IS THE MEAT!! Forgot to sigh, addy g in da houseAddy-g-indahouse 11:04, 28 August 2007 (UTC)

Scrap that, the rules are there, but they look way way too complicated, for a topic that is merely pre calculus. addy gAddy-g-indahouse 22:59, 28 August 2007 (UTC)

the explanations are WAY WAY to complicated, meaning anyone who wants to learn how to differentiate will look at it wil a expression similar to being clubbed over the head. I have many textbooks that have the rules written in this way, however it can be simplfied, without all the f'(gh'-1 etc.

simple eg product r(ule (x+1)^2(2x+1)^5

Let u=(x+1)^2 v=(2x+1)^5

dy/dx= u'v+v'u

simple as that, and without all the (f'(g'h)-1)gh-1

As per proofs, such proofs can be proved such that a newbie to calculus can just look at it and understand it, without calling in the aid of a rocket scientist.

regards addy g in da houseAddy-g-indahouse 11:04, 28 August 2007 (UTC)

I have no idea what you're talking about. This article does not mention the product rule, because it's an overview of the whole field of differential calculus and the product rule is only a small part of it. The product rule is briefly mentioned in derivative as

which seems pretty much what you want, and more fully in product rule. -- Jitse Niesen (talk) 01:34, 29 August 2007 (UTC)

[edit] Functions that are not lines

This edit ought to be undone. There has been discussion about this on the reference desk. I am not yet convinced that an infinite set can be bigger than another infinite set, plus that is not what the sentence intends to mean in the first place, as User:KSmrq pointed out. A.Z. 06:38, 30 September 2007 (UTC)

Fair enough. I dislike the "many functions of practical interest" though, because it is unnecessarily vague, and the expression "line function" is not used as far as I know. So I used another formulation which resolves the issue of what "most functions" means.

I have to think a bit about the next sentence, which reads "The derivative of f at the point x is the best linear approximation, or linearization, of f near the point x." I think this is an unfortunate way to put it. If linearization of f is the function then the derivative is a; these are not the same. -- Jitse Niesen (talk) 12:59, 30 September 2007 (UTC)

The problem seems to be that the derivative, when formulated abstractly, already encodes the value of the function: Given f : R → R, the derivative of f at a is a linear map f'(a) : T_aR → T_f(a)R. So by the very choice of domain and range, the derivative includes the point at which it's taken and the value of the function at that point. From this abstract perspective, it's entirely appropriate to say that the derivative is the linearization of f at a; but unless you introduce tangent spaces and begin talking in high-powered language, that statement is out of reach, and the linearization of f is the linear function f(a) + f'(a)(x-a) instead.

I've replaced the previous language with something that's a little looser to start with ("best possible approximation to the idea of the slope") and is completely precise at the end ("Together with the value of f at x, the derivative of f determines the best linear approximation"). I think this is better, but feel free to edit it as you like. 141.211.62.20 01:26, 18 October 2007 (UTC)