Talk:Function of several real variables

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Real coordinate space

You may reuse Real coordinate space #The domain of a function of several variables and some other pieces there, as well as make wikilinks back and fourth. Also, do not forget about category: Multivariable calculus. Incnis Mrsi (talk) 14:05, 26 June 2013 (UTC)[reply]

Done link and category, I'll continue writing later today. M∧Ŝc²ħε И_τlk 14:12, 26 June 2013 (UTC)[reply]

To do

Thanks for the creation of this article. This is a good thing for WP. However, this article is yet a stub, relatively to the amount of material that should be in it and is yet lacking. I'll use the template {{to do}} to summarize this lacking material. D.Lazard (talk) 04:24, 27 June 2013 (UTC)[reply]

A good list, but presumably some things (like the Taylor expansion, partial derivatives, Hessian matrix, real multivariable calculus) are to be mentioned and linked to, not to be covered in too much depth here. M∧Ŝc²ħε И_τlk 06:09, 27 June 2013 (UTC)[reply]

By now, I've at least scraped the surface of a number of entries in the list. Any corrections of my inaccuracies are appreciated in advance.

Maybe some examples could be removed but not sure which ones. The geometric examples are always nice for easy visualization (surfaces of conics and surfaces/volumes of certain 3d solids). Considering the recent posts at Wikipedia talk:WikiProject Mathematics#Linear function, Linear Equation, Linear Inequality full of errors and inconsistencies and "matheese" about "linear equations" and "linear functions", etc. we should at least keep the plane and hyperplane examples... as well as non-linear examples for contrast. The inclusion of a variety of examples in physics/engineering/applied maths is essential. ~~For compactness maybe we could tabulate some examples but it would not be encyclopaedic to do so...~~ Will look at trimming later. M∧Ŝc²ħε И_τlk 10:08, 28 June 2013 (UTC)[reply]

The article is desperate for diagrams, which are coming shortly. M∧Ŝc²ħε И_τlk 11:12, 29 June 2013 (UTC)[reply]

Multiple issues

User:Maschen has done a hard work in writing from scratch such a fundamental article. Nevertheless, in its present state the article has multiple issues. Some of them are easy to solve, but other are more difficult. Here are the main issues:

Level of the target reader: One may consider that the reader of this article has some knowledge of what is a function and what is a function of one real variable. Otherwise he would not arrive to this article. In fact, when searching for "function", the first answer is Function (mathematics) and when searching for "function of", Function of a real variable appears before the present article. It follows from this remark that the section "Introduction" is off-topic and most of the section "General definition (real-valued functions of several real variables)" must be simplified and rewritten to remove over detailed explanations of the similarity between univariable and multivariable cases and emphasizing on the differences.
Level of the target reader (2): Although on may suppose that the reader knows something about univariable case, it is essential to suppose that he does not know anything about the multivariate case. Therefore the definition of the continuity and the differentiability must be given explicitly (this is not the case) and illustrated by examples showing that the continuity in each variable does not implies continuity, and that differentiability in each variable does not implies differentiability.
Confusion in the terminology: The article uses in the definitions many terms that either do not have any formal definition or have a formal definition but only in a different context. Such are: "dependent variable", "independent variable", "continuously varying variable". Moreover, the article is confusing by not clearly distinguishing a function, its graph and the equation of its graph. This confusion is common when teaching kids (I do not know if it is pedagogically a good thing), but must be avoided in a encyclopedia.

There are many other issues. As they are less fundamental, either I'll correct them by editing directly the article or they will be the object of another post. D.Lazard (talk) 14:33, 30 June 2013 (UTC)[reply]