# Talk:Calculus

## Unwrite

I propose tht instead of a rewrite, we unwrite this article. Looking at the prose structsure from bottom to top and, in that order, we correct what should be.

• What is this, I don't even.

## Rewrite

I have been comparing this article to the English and French articles on it and it does not seem to describe calculus, I was wondering if anybody else thought this could use a rewrite. Oysterguitarist 00:20, 21 November 2007 (UTC)

I will take a look, and might be bold. Baccyak4H (talk) 17:47, 22 January 2008 (UTC)

I'm being very bold and rewriting the whole thing - I've tutored for years and taught kids in a school last year, including many who did not understand more than very basic algebra but had made it to the 11th grade. Probably as I go I'll split the bits off into the sub-articles and just have the final conclusions and the rules in this article. I'd appreciate anyone (especially beginning calculus students) having a look over this to make sure I've levelled it correctly - most of my work is in person so some nuances may be lost in the written version. Orderinchaos (talk) 06:40, 31 December 2008 (UTC)

Just noting that I am still working on it - I'll do a section on integral calculus and the fundamental law, and write a new article on integral calculus as an offshoot from this, as I have for differential calculus. Orderinchaos (talk) 21:58, 9 January 2009 (UTC)

aren't these lines: "They then chose points on either side of the point they were interested in and worked out tangents at each. As the points moved closer together towards the point they were interested in, the slope approached a particular value as the tangents approached the real slope of the curve," incorrect? how would they work out tangents at those other points? shouldn't it be that they picked other points along the curve, connected them with a line to the point they were interested in and found the slope of that line - the secant line between the points - and as the other points got closer to the point of interest, the slope of the secant line approached the slope of the tanget. that IS after all what using the limit process behind differentiation is doing. if whoever is writing this article doesn't address it, i'll make changes in a few days.

I wouldn't oppose that change if it makes it clearer. I think I probably got tangled up trying to explain it. :) Orderinchaos (talk) 07:33, 7 March 2009 (UTC)

Calculus is not the study of things that change over time. It can be used to study those things, but it can also study how things change over space, or over heat, or over anything else that can be described with numbers. Time is one of the most useful applications, but it is not the only one nor is it necessary or even helpful to describe time in calculus. Granted, derivatives are "rates of change", but a rate of change is just how the number(s) change over something, it could be changes over time, over space, or over some other quantity. Could someone more familiar with simple articles correct this? Thanks. 129.59.124.121 (talk) 20:16, 22 April 2010 (UTC)

## Main Idea in Calculus

Following the above comment regarding the applications of calculus extending well beyond time-rates of change, I would say that the central concept of calculus is *not* the fundamental theorem of calculus (FTC), rather, the central concept of the subject is known, in technical terms as convergence. I think the essence of convergence can be loosely conveyed in the idea that, on small scales, it is impossible to tell the difference between straight and curvy lines. This approach explains the use of (and need for!) limits in the definition of both the derivative and the integral and is really the main idea of calculus.

On a related note, it would be relatively easy to demonstrate this with an animated image that would cover up a curved and straight line showing that it is impossible to distinguish them when only a small part is showing, then revealing both lines to show that one is straight and the other curve.