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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 UTC7, 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." >> >> >> > >> > http://mpec.sc.mahidol.ac.th/RADOK/physmath/mat6/calc2.htm >> >> >> > >> > 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 illformed 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/radok/physmath/MAT6/startDIall.htm >> >> 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.



