Infinitesimal analysis, once a synonym for calculus, is now viewed as a
technique for studying the properties of an arbitrary mathematical
object by discriminating between its standard and nonstandard
constituents. Resurrected by A. Robinson in the early 1960's with the
epithet 'nonstandard', infinitesimal analysis not only has revived the
methods of infinitely small and infinitely large quantities, which go
back to the very beginning of calculus, but also has suggested many
powerful tools for research in every branch of modern mathematics.
The book sets forth the basics of the theory, as well as the most recent
applications in, for example, functional analysis, optimization, and
harmonic analysis. The concentric style of exposition enables this work
to serve as an elementary introduction to one of the most promising
mathematical technologies, while revealing up-to-date methods of
monadology and hyperapproximation.
This is a companion volume to the earlier works on nonstandard methods
of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN
0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by
S.S. Kutateladze (2000), ISBN 0-7923-6619-0