From Newton’s fluxions to virtual microscopes

@article{Bair2006FromNF,
  title={From Newton’s fluxions to virtual microscopes},
  author={J. Bair and V. Henry},
  journal={Teaching Mathematics and Computer Science},
  year={2006},
  volume={5},
  pages={377-384}
}
  • J. Bair, V. Henry
  • Published 2006
  • Mathematics
  • Teaching Mathematics and Computer Science
The method of fluxions was originally given by Newton among others in order to determine the tangent to a curve. In this note, we will formulate this method by the light of some modern mathematical tools: using the concept of limit, but also with hyperreal numbers and their standard parts and with dual numbers; another way is the use of virtual microscopes both in the contexts of classical and non standard analysis. 
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References

SHOWING 1-10 OF 13 REFERENCES
Nonstandard Analysis
TLDR
The construction of nonstandard extensions could provide a rigorous foundation for the use of infinitesimals in basic analysis, and NSA has become an active branch of research in its own right. Expand
Non-Standard Analysis
1. As early as 1934 it was pointed out by Thoralf Skolem (see [17]) that there exist proper extensions of the natural number system which have, in some sense, ‘the same properties’ as the naturalExpand
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand
Tangentes aux coniques : méthodes passées
  • présentes et à venir, Mathématiques et Pédagogie 152
  • 2005
Nouvelle approche pour introduire la notion de tangente à une courbe
  • Mathématiques et Pédagogie 145
  • 2004
Analyse mathématique I : convergence
  • fonctions élémentaires, Springer-Verlag, Berlin Heidelberg
  • 1998
Analyse mathématique I : convergence, fonctionsélémentaires
  • 1998
Elementary Calculus
  • Prindle, Weber & Schmidt Inc., Boston
  • 1976
...
1
2
...