# How common is the use of the term “primitive” to mean “antiderivative”?

I don't know if this should actually be asked on the English stackexchange. It seemed like I would find better answers here.

I have all but finished an undergraduate degree in mathematics in the United States, but I have never once heard the term "primitive" to mean "antiderivative" until recently, when someone from Europe pointed it out to me. According to him, it's a common term there. So I was wondering if people could give me an idea of how common this term is, and where. I know for sure that if someone says "primitive" to a math student in the US, that the student won't know what he is talking about. Does the reverse hold for "antiderivative" (or the also common "integral") elsewhere?

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Spivak uses the term in his Calculus, which I think is quite popular in the US. –  Dylan Moreland Jun 26 '11 at 3:49
In Romania, from where I am from, the term primitive is used. I thought at first that the term primitive is not used in English, but as mentioned, there are books in English which use it. –  Beni Bogosel Jun 26 '11 at 11:11
I'm thinking that the standard term was "primitive", but at some point an American textbook writer invented the term "antiderivative", which has gradually become the most popular in calculus textbooks. –  GEdgar Jun 26 '11 at 12:46
Re: last question. I think antiderivative is pretty self-explanatory (even if I find the word a bit ugly and unnecessarily complicated). Even if I had never heard it before, I would immediately have thought of an integral. (my native language is German and there Stammfunktion is the common term). –  t.b. Jun 27 '11 at 2:15
Here in Argentina (spanish language) the term "primitiva" is used, almost exclusively. –  leonbloy Jun 27 '11 at 2:42

Apostol's "Calculus" volume 1 uses "primitive" in that sense 41 times, whereas "antiderivitive" is only used 4 times. Two of those are in the main text, always as part of an "or antiderivative" after the term "primitive", and the other two are in the index.

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Upvoted for cunning use of ctrl-F. –  barf Jun 26 '11 at 11:59

In complex analysis the antiderivative is often refered to as the primitive.

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Ah, that may be. I've yet to take complex analysis (I will have it next semester). –  asmeurer Jun 26 '11 at 5:58
I checked the book I will be using, "Complex Variables, Second Edition" by Ablowitz and Fokas, and "antiderivative" is in the index twice, but not "primitive". Furthermore, I used Google Books to search for the word "primitive" within the book, and it found no results (but four results for "andiderivative"). So I think you are wrong about it being used universally in complex analysis. –  asmeurer Jun 27 '11 at 4:09
i said often used. not universally. see ahlfors or conway –  Digital Gal Jun 29 '11 at 3:21
I've since taken two semesters of complex analysis and my professor never used the term (anti-derivatives aren't even that important in the field anyway). –  asmeurer Jun 17 '12 at 3:07

I think this is due to Richard Courant. In his 2 volume book Differential and Integral Calculus, he uses the term 'primitive' to mean antiderivative.

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It's certainly a lot older than Courant. See jeff560.tripod.com/mathword.html which traces "primitive" back to Lagrange in 1797. For "anti-derivative" the first reference they have is 1903. –  Robert Israel Jun 26 '11 at 14:25

I can just say that "the primitive function" (primitivní funkce) is the only official name of this object in Czech. Also, I think that the most standard English term is not "antiderivative" but rather "indefinite integral".

http://en.wikipedia.org/wiki/Antiderivative

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"Integral" is used more often (ambiguously), but the rigorous usage always uses "antiderivative". Rigorously, I think the difference might be that "indefinite integral" refers the the family of all possible antiderivatives (F(x) + C), whereas "antiderivative" refers to any one of those (F(x) is "an antiderivative" of f(x)). –  asmeurer Jun 26 '11 at 5:57
Though I don't think it's exactly standard, I like the use (saw this in Apostol, I think?) of "indefinite integral" to specifically mean $F(x)=\int_a^x f(t)dt$ for some f and a. Of course this turns out to be the antiderivative when f is continuous, but... –  Harry Altman Jun 26 '11 at 13:53

In the Dutch language, the antiderivative is known as the "primitieve".

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I know it as "primitieve". –  Jonas Teuwen Jun 26 '11 at 10:04
While we're at what it's called in other languages: In Danish it's called "stamfunktion" as in "f stems from F" –  kahen Jun 26 '11 at 10:28
In French it's only called "primitive" too, there's no equivalent for "antiderivative". –  Najib Idrissi Jun 26 '11 at 10:53
@Jonas, You are right, that is emberassing –  Thomas Rot Jun 26 '11 at 21:56
@kahen: (Almost) the same in German: Stammfunktion –  t.b. Jun 26 '11 at 22:36