User talk:Cronholm144/Integral

Nice to see you've beefed things up appropriately in terms of coverage (though, of course, some of the sections are skeletal for now). At this stage I'm more worried about accessibility to a general audience, at least as far as the beginning of the article goes (it is reasonable to spin off into more complex/inaccessible topics as the article progresses). I want to: (a) Completely rewrite the introduction. It is a strange hash of overly specific examples, and hopelessly vague generalities right now. To do that, however, it will be helpful to... (b) Block out a decent finalised outline for the article. Further to that point I am hoping to write: (c) An "intuitive idea" section (still looking for a good title) which provides the general concept in layman's terms, and can proceed a "formal definition" section which really ought to be a more rigorous version of "definition" as it currently stands.

So, moving forward, my current idea for an outline (which I am pleased to see agrees reasonably with what you've already done) is:

Introduction

Informal explanation
Formal definition
- Riemann integral
- Lesbesgue integral
- Other integrals
History
Applications of integration
Basic integrals (that is, scalar valued functions over the reals)
Computing integrals
- Techniques of integration
- Numerical approximation
- Symbolic integration
Multiple integrals
Line and surface integrals
- Line integrals
- Surface integrals
Integrals in complex analysis
Integration and measure theory
Integration of differential forms
de Rahm cohomology

I am, of course, open to discussion on this. Thanks. -- Leland McInnes 16:59, 4 June 2007 (UTC)[reply]

Looking at your outline, I'd say the it builds very nicely for the uninformed reader (starting very friendly and simple and ending by destroying them... assuming that they even read that far). Seriously though, I think we should, when crafting the latter part of the article, remember our audience first and foremost. If we do it right they may not run away until they hit measure theory.

Intuitive Ideas and concepts are usually termed "informal discussion" or "general discussion" but I don't really like these either. Perhaps we can cheat and merge the intuitive parts with the lead. Either way, I think that the formal discussion is going to be the most difficult part to flesh out. Because, to be truly formal, you will have to approach integration form a very general place and this might serve to confuse the reader; hopefully the informal discussion you propose will be enough to prepare them.

Feel free to edit here as much as you want to flesh out your ideas. I regret that I have been distracted with writing algebra articles lately, so I have not attended to this sandbox since its creation. I am going to alert the other editors to this creature's existence, hopefully it will encourage some real improvement. Cheers--Cronholm¹⁴⁴ 19:19, 4 June 2007 (UTC)[reply]

I think in your means of calculating integrals you should mention stokes theorum, and the divergence theorum, since these tecniques are prevalent in undergraduate physics/applied maths courses. Phil 20686 15:45, 10 June 2007 (UTC)[reply]

Sounds like decent idea. I haven't really touched that section yet, but I'll try to keep this in mind when I get to it. -- Leland McInnes 19:16, 11 June 2007 (UTC)[reply]