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I recently edited the "multivariate-calculus" tag, and described it as follows:

For questions about teaching calculus with functions of more than one variable (also perhaps known as "Vector calculus" or "Calculus 3").

I now see there is a "vector-calculus" tag. They're both infrequently-used for now (one question under multivariate, two under vector), but I'm sure they'll be more popular in the future. So, I thought it helpful to bring this up now. I will post my proposed "solution" below.

Consider upvoting this post to be promoting the discussion, and upvoting an answer to be supporting that viewpoint.

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I agree. I have merged the two tags, and I have made "multivariable calculus" a synonym for "vector calculus".

These two names seem equally good to me, but "vector calculus" has been used twice so far, and "multivariable calculus" has only been used once, so "vector calculus" wins.

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I believe "vector-calculus" should be the tag we use, and would like to see all appropriate uses merged into this one.

First, "multivariate" is a little cumbersome and might sound confusing to a non-native-English speaker, yet "vector" translates well (I think).

Second, it's common amongst students (and, thus, teachers) to refer to a course that predominantly teaches the calculus of multi-variable functions as "vector calc", as opposed to "multivariate calc". I have also heard "multi-variable calc" or "3-d calc" or "calc of several variables", and so on, but "multivariate" is not as common, in my experience. Accordingly, I don't anticipate that new users with questions about this topic will think to search for the "multivariate" tag, and will rather look for "vector-calc".

To update the tag wiki to be appropriate for "vector-calculus", I propose the following:

For questions about teaching calculus involving vectors and functions of more than one variable. Such a course might be known as "Vector Calc" or "Calc 3" or "Multi-variable Calc".

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    $\begingroup$ I agree. I'm in favor of "multivariable calculus" though. $\endgroup$ – Mark Fantini Apr 2 '14 at 9:44
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I have no strong opinion one way or the other, but the distinction between the terms in my lexicon is as follows:

  • multivariate calculus: calculus of functions of several variables: for example, partial derivatives of functions $f: \mathbb{R}^2 \rightarrow \mathbb{R}$
  • vector calculus: calculus of vector fields. This includes line and surface integrals, stokes and divergence theorems etc... in a more advanced course, the further theorems of Greene, some potential theory and so forth.

Technically, vector calculus uses multivariate calculus. Sometimes, the calculus of vector valued functions of a real variable will also be called vector calculus. The textbooks on vector calculus are typically just about the very last bit of what is commonly called calculus III in current American universities. So, in short, I think they are separate terms, and I would gravitate towards vector calculus labeling the more advanced questions attached to line and surface integrals whereas multivariate calculus is simply the calculus of functions of several variables. As a typical pattern, I might expect many questions with the vector calculus tag to also have the multivariate tag, but many multivariate questions would not warrant the vector calculus tag.

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