Talk:List of calculus topics

Untitled
Actually I think alphabetizing destroys the logical order of the topics, of help to students. Revert, please.

Charles Matthews 08:12, 10 Oct 2003 (UTC)

Umm... done. Evil saltine 09:29, 10 Oct 2003 (UTC)

Removed these links;

Fractional calculus

 * Fractional calculus
 * Differintegral
 * initialization of the differintegrals
 * basic properties of the differintegral
 * basic rules of differintegration

These belong with Fourier theory, really.

Charles Matthews 17:59, 10 Oct 2003 (UTC)

Why does it belong with fourier theory? The only relation I see is that one way, out of many ways, to take a fractional derivative, is by tranforming it into fourier space, translating it, and transforming it back. But this can be done with regular calculus, so by that logic, regular calculus belongs in fourier theory as well.

I really don't see what fractional calculus has to do with fourier theory. The concepts are completely independant. Fractional calculus is not even concerned with orthogonal systems.

Furthermore, I fail to see how fractional calculus is not calculus. It's used on the same problems and for the same purposes, and it works the same way. It's a generalization of the derivative/antiderivative to arbitrary order. One still "integrates" or "differentiates"; one still measures an event space with respect to another event space. (such as dt1/dt2).

-Kevin Baas 2003.10.12

Fractional calculus is a topic that belongs in list of topics in real analysis. Just as complex differentiation and integration in a list of topics in complex analysis. Both of these pages may be created shortly.

The connection with Fourier theory is explicit in pseudo-differential operator theory (which is one modern approach to fractional calculus, though not the only one). By going to Fourier transforms one diagonalises the differentiation operator (-id/dx for preference, to get something self-adjoint). Then apply spectral theory. You can for example multiply Fourier series by sqr(n) to get a square root of the differentiation operator. This is meaningful for distributions. The classical Riemann-Liouville version extracts from this complex of ideas a part that can be done by singular integral operators; but I think any professional in the real analysis field could explain (I'm not one) that this is an expected aspect of the theory.

Please understand that the aim of this page is essentially pedagogic, to organise (and thereby also help upgrade) the contributions in Wikipedia to basic classical calculus topics.

This is in line with many comments on keeping a reasonable level, on entry topics for college students.

Charles Matthews 08:30, 12 Oct 2003 (UTC)

I respect the aim at pedagogy and think that it represents "values in the right place".

At the same time, I feel that there is not enough awareness of fractional calculus, and that it is a subject that is becoming more important. (Fractional control theory, fracture analysis, and rheology, and a few examples.) I also feel that contemporary paradigm shifts will make fractinal caclulus more "intuitively natural" in the near future, and that it's teaching will become more frequent and the level that it is considered less "advanced".

But I do not know what the popular mythology for percieving the structure of mathematical concepts is, and I don't consider it conducive to mess with an organization that isn't even substantially in place; the mathematics pages still need a lot of work, and there's no value in making it a hassle.

In conclusion, I concede the introduction to the subject here for the sake of pedagogy, as you mentioned, from the angle of the contemporary mythology on the structure of mathematical concepts. (which is far more developed than the one which is currently emerging) Yet I ask that fractional calculus not be "pushed aside" in general. It seems to me that it is a subject that has been undeservedly neglected.

-Kevin Baas 2003.10.12

I've put a place for it on the new list of real analysis topics page - still working on that, since to find everything I have to go through all the backlinks.

Charles Matthews 15:58, 12 Oct 2003 (UTC)


 * Thanks. :) -Kevin Baas 2003.10.12

Limits
This article lists "Limits" as a subsection of pre-calculus. Is this "right"? I take limits to be the heart of calculus, rather than a pre-calculus topic. -- Meni Rosenfeld (talk) 14:50, 22 January 2006 (UTC)