Generalizing difference quotients to other operations
Dave L. Renfro
differentiation notions based on replacing difference quotients
with other operation pairs, such as quotient roots.
http://groups.google.com/group/sci.math/msg/2e8b2bd9d7db03cf
I've since come across a couple more references (items [6] and [10]
below, by accident) and I thought it would be useful to archive all
the references together in a sci.math post. I'm beginning a new
thread because google's "statue of limitations" for replying to
a post has expired for my earlier post.
The references below are ordered by publication date.
[1] Robert Edouard Moritz, "Quotientiation, an extension of the
differentiation process", Proceedings of the Nebraska Academy
of Sciences (1901), 112-117. [JFM 33.0303.01]
http://www.emis.de/cgi-bin/JFM-item?33.0303.01
[2] Robert Edouard Moritz, "Generalization of the differentiation
process", American Journal of Mathematics 24 (1902), 257-302.
[JFM 33.0302.02]
http://www.emis.de/cgi-bin/JFM-item?33.0302.02
[3] Allen Fuller Carpenter, "Geometrical interpretations of
quotientiation and its inverse", Bulletin of the American
Mathematical Society (2) 17 (1911), 446. [JFM 42.0312.01]
http://www.emis.de/cgi-bin/JFM-item?42.0312.01
[4] Michael Grossman and Robert Katz, NON-NEWTONIAN CALCULUS,
7'th printing, Mathco (Box 240, Rockport, Massachusetts)
1979, viii + 96 pages. [First printed in 1972.]
[MR 55 #3180; Zbl 228.26002; ZDM 1982a.00259]
http://www.emis.de/cgi-bin/MATH-item?0228.26002
http://tinyurl.com/9vtvp [ZDM review]
http://tinyurl.com/aawlk [scanned pages from google-books]
http://www.google.com/search?as_epq=non+newtonian+calculus
http://groups.google.com/groups?as_epq=non+newtonian+calculus
[5] Michael Grossman, THE FIRST NONLINEAR SYSTEM OF DIFFERENTIAL
AND INTEGRAL CALCULUS, Archimedes Foundation, 1979,
xi + 85 pages. [MR 80m:26005; ZDM 1982a.00243]
http://www.emis.de/cgi-bin/MATH-item?0443.26005
http://tinyurl.com/73rwo [ZDM review]
http://tinyurl.com/dzpx5 [scanned pages from google-books]
[6] Michael Grossman, "An introduction to non-Newtonian calculus",
International Journal of Mathematical Education in Science
and Technology 10 #4 (Oct.-Dec., 1979), 525-528.
[Zbl 418.26008; ZDM 1982a.00259]
http://www.emis.de/cgi-bin/MATH-item?0418.26008
http://tinyurl.com/9vtvp [ZDM review]
[7] Jane Grossman, Michael Grossman, and Robert Katz, THE FIRST
SYSTEMS OF WEIGHTED DIFFERENTIAL AND INTEGRAL CALCULUS,
Archimedes Foundation, 1980, viii + 55 pages.
[MR 81k:26003; Zbl 443.26005; ZDM 1982a.00248]
http://www.emis.de/cgi-bin/MATH-item?0443.26005
http://tinyurl.com/e2km3 [ZDM review]
http://tinyurl.com/7l5n5 [scanned pages from google-books]
[8] James R. Meginniss, "Non-Newtonian calculus applied to
probability, utility, and Bayesian analysis", Proceedings
of the American Statistical Association: Business and
Economics Statistics Section (1980), 405-410.
[9] Michael Grossman, BIGEOMETRIC CALCULUS: A SYSTEM WITH A
SCALE-FREE DERIVATIVE, Archimedes Foundation, 1983,
vii + 100 pages. [MR 84h:26003; ZDM 1986l.06868]
http://tinyurl.com/c58dn [ZDM review]
http://tinyurl.com/9kc4g [scanned pages from google-books]
[10] Anthony Quas, "Ratio derivatives", Mathematical Spectrum
19 #3 (1986/87), 72-75. [ZDM 1988e.00859]
http://tinyurl.com/8cfqx [ZDM review]
Dave L. Renfro