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Topic: 2.45 - What some PhDs said about differentials.
Replies: 1   Last Post: Aug 4, 2014 4:24 PM

 David C. Ullrich Posts: 3,555 Registered: 12/13/04
Re: 2.45 - What some PhDs said about differentials.
Posted: Aug 4, 2014 4:24 PM

On Sun, 03 Aug 2014 21:45:59 -0700, John Gabriel wrote:

> On Sunday, 3 August 2014 21:54:02 UTC+2, FredJeffries wrote:
>> On Sunday, August 3, 2014 11:48:29 AM UTC-7, John Gabriel wrote:
>>

>> > "However, we must guard ourselves against thinking of dx as an
>> > infinitely small quantity or infinitesimal, or of the integral the
>> > sum of an infinite number of infinitely small quantities. Such a
>> > concept would be devoid of any clear meaning; it is only a naïve
>> > interpretation of what we have previously carried out with
>> > precision."

>>
>>

>> >

>>
>>

>> >
>> > Notice, Radok claims "devoid of any clear meaning". He also states
>> > that such thought is "only a naïve interpretation of what we have
>> > previously carried out with precision", that is, as a result of the
>> > fundamental theorem of calculus.

>>
>>
>>
>> This is an extremely interesting usage of the word "previously"
>> inasmuch as the phrase you quote is in section 2.1. whereas the
>> fundamental theorem of calculus is not introduced until section 2.4

>
> And that makes no difference whatsoever. The ill-formed concepts are to
> used to define the integral which is evaluated using the fundamental
> theorem of calculus (long before it is officially stated).

Nope. FTC is not used in evaluating those integrals.

>
>

>>
>>
>> By the way, the Ph.D. author of the book from which this quote is
>> pulled is Richard Courant and the book is his "Differential and
>> Integral Calculus"
>>
>>
>>
>>
>> http://mpec.sc.mahidol.ac.th/library/oldbooks

>
> Courant is not even half the mathematician that most think he is.
> Anyway, Radok's most important work was his translation of a Russian
> book on boundary value problems in differential calculus.