Re: Non-Newtonian Calculus website at http://www.angelfire.com/ma4/nnc

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This website presents a brief account of the non-Newtonian calculi,
which are markedly different from the classical calculus and provide a
wide variety of mathematical tools for use in science and engineering.
  
The first publication on non-Newtonian calculus was the book
"Non-Newtonian Calculus" (QA303.G88) by Michael Grossman and Robert
Katz.  It
includes discussions of nine specific non-Newtonian calculi, the
general theory of non-Newtonian calculus, and heuristic guides for the
application thereof.  Detailed accounts of two specific non-Newtonian
calculi are presented in Grossman's books "The First Nonlinear System
of Differential and Integral Calculus" (QA303.G878) and "Bigeometric
Calculus: A
System with a Scale-Free Derivative."

Each non-Newtonian calculus, as well as the classical calculus, can be
"weighted" in a manner explained in the monograph "The First Systems
of Weighted Differential and Integral Calculus" by Jane Grossman,
Michael Grossman, and Robert Katz.  Natural outgrowths of the weighted
calculi are the systems of meta-calculus, which are described in Jane
Grossman's monograph "Meta-Calculus: Differential and Integral."

In their monograph "Averages: A New Approach," Jane Grossman, Michael
Grossman, and Robert Katz showed how the averages (of functions) that
arose naturally in the development of the non-Newtonian calculi can be
used to construct an infinite family of means of two positive numbers.

The first application of non-Newtonian calculus was made by Professor
James R. Meginniss of the Claremont Graduate School and Harvey Mudd
College.  In his article "Non-Newtonian Calculus Applied to
Probability, Utility, and Bayesian Analysis" (Proceedings of the
American Statistical Association), he used non-Newtonian calculus to
develop a new theory of probability suitable for the analysis of human
behavior and decision making.

We can only speculate as to future applications of the non-Newtonian
calculi.  Perhaps they can be used to define new scientific concepts,
to yield new or simpler scientific laws, to solve heretofore unsolved
problems, or to formulate and solve new problems.

Note. Those six books/monographs on non-Newtonian calculus and related
matters are available at some academic libraries, public libraries,
and (internet) used-book stores.