Re: Wolfram, meet Stefan and Boltzmann

*To*: mathgroup at smc.vnet.net*Subject*: [mg117507] Re: Wolfram, meet Stefan and Boltzmann*From*: Robert Rosenbaum <robertr at math.uh.edu>*Date*: Mon, 21 Mar 2011 06:14:51 -0500 (EST)

I should probably let this tangent topic die off, but I thought I'd give my two cents. "Anti-derivative" is a useful and frequently used term. I use it often when teaching calculus and it's also used in textbooks. However, the phrase "the anti-derivative" is meaningless since anti-derivatives are never unique. When teaching, I always say "an anti-derivative," lest the students become confused. Best, Robert On Mar 20, 2011, at 4:54 AM, Andrzej Kozlowski wrote: > "Anti-derivative" is a somewhat newer term than the very old "indefinite integral" and is used particularly often in complex analysis and in more al= gebraic contexts (for example differential algebras, where the word "indefi= nite integral" would definitely sound unsuitable). For example "anti-deriv= ative" is used in the classic "Complex Analysis" by Lars Ahlfors. > > Anti-derivative is also used in textbooks of real analysis where the auth= ors are particularly careful to emphasise concepts rather than computing te= chniques. > For example, it is also used in Apostol's very popular "Calculus", althou= gh it is given there as the alternative (second) choice - the first choice = being "the primitive" of a function (the word "indefinite integral" is not = even mentioned). > > Although the words "antiderivative" and "primitive" are newer than "indef= inite integral" they are not really very new - the oldest book I have that = uses these terms seems to be "The theory of functions of a real variable" b= y L.M.Graves, which was published in 1946. > > One reason why the words "primitive" and "anti-derivative" are preferred = to"indefinite integral" is that they emphasise the non-trivial nature of th= e fundamental theorem of calculus. To say that you can compute the definite= integral by evaluating an indefinite integral at the limits of integration= and subtracting sounds almost like a tautology; to say that you can comput= e the integral of a function by finding and evaluating its primitive, sound= s like the profound result that it actually is. > > > Andrzej Kozlowski > > > On 19 Mar 2011, at 11:20, AES wrote: > >> In article <ilve3r$emn$1 at smc.vnet.net>, SigmundV <sigmundv at gmail.com> >> wrote: >> >>> It also astonished me that AES is not familiar with the term >>> 'antiderivative'. The derivative of the antiderivative is the function >>> itself. >> >> Pretty obvious what it means, of course. But: >> >> 1) "Antiderivative" doesn't appear in the New Oxford American >> Dictionary; "indefinite integral" does. >> >> 2) The MIT Math Department's online "Calculus for Beginners" course >> says: >> >> 16.1 The Antiderivative >> >> The antiderivative is the name we sometimes (rarely) give >> to the operation that goes backward from the derivative of >> a function to the function itself . . . The more common name >> for the antiderivative is the indefinite integral. This is the >> identical notion, merely a different name for it. >> >> 3) I'm 250 miles from my home library at the moment, so can't look in >> the indexes of Morse and Feshbach or comparable classics; but amazon.com >> has an online searchable listing for Courant and Hilbert, Methods of >> Mathematical Physics, and "antiderivative" doesn't appear in its index, >> or anywhere else in the book. >> >> And so on . . . >> >

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**Re: Wolfram, meet Stefan and Boltzmann**

**Re: Wolfram, meet Stefan and Boltzmann**