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Topic: The New Calculus
Replies: 12   Last Post: Aug 28, 2014 5:38 PM

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Louis Talman

Posts: 4,605
Registered: 12/27/05
Re: The New Calculus
Posted: Aug 25, 2014 11:47 PM
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Elementary calculus can be done without limits, though I don't see the
point in trying.

And Gabriel's pretty far from accomplishing it.

See "Calculus Unlimited," by Marsden & Weinstein.


On Mon, 25 Aug 2014 17:55:52 -0600, Robert Hansen <bob@rsccore.com> wrote:

>
> On Aug 25, 2014, at 5:13 PM, Dave L. Renfro <renfr1dl@cmich.edu> wrote:
>

>> First, it's not clear to me what the role of m and n are.
>> Are we to take the double limit as (m,n) --> (0,0) (and if so, do we
>> assume the ratio m/n is fixed during this process)? Are we to take
>> an iterated limit in which we take the limit m --> 0 for fixed nonzero
>> values of n and then follow-up with a limit as n --> 0 (or reverse
>> the order)?

>
> I feel enough shame as it is for posting the link.
>
> 1. I am certain he doesn?t intend for us to take a limit of any kind
> because that is the whole point of inventing a new calculus without
> limits.
>
> 2. He seems to be saying (in the PDFs) that since Q(m.n), which is all
> the factors including m and n after you apply his asymmetrical
> difference quotient, must equal zero when the secant and tangent have
> the same slope, that we can go ahead and just ignore them. In other
> words, m and n don?t matter.
>
> For example, using the difference quotient we are familiar with, well, I
> am familiar with (you are obviously familiar with many more)?
>
> For f = x^2
>
> delta-y/delta-x = ((x+h)^2 - x^2) / h
>
> = (x^2 + 2xh + h^2 - x^2) / h
>
> = 2x + h
>
> h = 0
>
> f?(x) = 2x
>
> See, no limits.:)
>
> Bob Hansen



- --
- --Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver

<http://rowdy.msudenver.edu/~talmanl>



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