[FOM] practical use of infinitesimals

[Vladik Kreinovich]

Dear Friends, 

In view of a recent posting on a non-standard models congress, it may be of 
interest to the FOM community that infinitesimals, in the form of appropriate 
power series, are used in efficient algorithms for computing the ranges of 
functions and in describing dynamical systems ranging from supercolliders to 
checking whether an nearby-flying asteroid hits the Earth. 

For details, see webpage of Martin Berz http://bt.pa.msu.edu/berz/ and 
references therein. In particular, connection to
infinitesimals is described in the following papers:

Cauchy Theory on Levi-Civita Fields
M. Berz, Contemporary Mathematics, American Mathematical Society, 319, 39-52
(2002),
Proc. Seventh Intern. Conf. Non-Archimedean Analysis
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rscni02

Measure Theory and Integration on the Levi-Civita Field
K. Shamseddine and M. Berz, Contemporary Mathematics, American Mathematical
Society, 319, 369-387 (2002)
Proc. Seventh Intern. Conf. Non-Archimedean Analysis
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rsmni02

Intermediate Values and Inverse Functions on Non-Archimedean Fields
K. Shamseddine and M. Berz, Int. J. Math. and Math. Sciences, 30(3), 165-176
(2002)
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rsijmms01

Analytical and Computational Methods for the Levi-Civita Field
M. Berz, Lecture Notes Pure Appl. Math., Proc. Sixth Intern. Conf.
Non-Archimedean Analysis, 21-34,
Marcel Dekker (2000)
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rsio00

Vladik