Re: Wolfram, meet Stefan and Boltzmann

*To*: mathgroup at smc.vnet.net*Subject*: [mg117501] Re: Wolfram, meet Stefan and Boltzmann*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Mon, 21 Mar 2011 06:13:46 -0500 (EST)

"Antiderivative" was certainly in use when I studied calculus in the early 1970s. I think it is the better word when it refers to a function with a name or formula, where "indefinite integral" may be more general, but less satisfying. The difference is informal, I think, more connotation than definition. Bobby On Sun, 20 Mar 2011 04:54:05 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl> 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 > algebraic contexts (for example differential algebras, where the word > "indefinite integral" would definitely sound unsuitable). For example > "anti-derivative" is used in the classic "Complex Analysis" by Lars > Ahlfors. > > Anti-derivative is also used in textbooks of real analysis where the > authors are particularly careful to emphasise concepts rather than > computing techniques. > For example, it is also used in Apostol's very popular "Calculus", > although 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 > "indefinite 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" by 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 > the 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 compute the integral of a function by finding and evaluating its > primitive, sounds 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 . . . >> > -- DrMajorBob at yahoo.com

**Re: PopupWindow vs EventHandler**

**Re: StreamPlot or streamlines in 3D?**

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

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