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Re: Wolfram, meet Stefan and Boltzmann

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  • Subject: [mg117501] Re: Wolfram, meet Stefan and Boltzmann
  • From: DrMajorBob <btreat1 at>
  • Date: Mon, 21 Mar 2011 06:13:46 -0500 (EST)

"Antiderivative" was certainly in use when I studied calculus in the early  

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  


On Sun, 20 Mar 2011 04:54:05 -0500, Andrzej Kozlowski <akoz at>  

> "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>, SigmundV <sigmundv at>
>> 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
>> 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

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