Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
Education
»
mathteach
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
The New Calculus
Replies:
12
Last Post:
Aug 28, 2014 5:38 PM




Re: The New Calculus
Posted:
Aug 25, 2014 11:47 PM


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 followup 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 > > deltay/deltax = ((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>



