This research monograph considers the subject of asymptotics from a
nonstandard view point. It is intended both for classical
asymptoticists - they will discover a new approach to problems very
familiar to them - and for nonstandard analysts but includes topics
of general interest, like the remarkable behaviour of Taylor
polynomials of elementary functions. Noting that within nonstandard
analysis, "small," "large," and "domain of validity of asymptotic
behaviour" have a precise meaning, a nonstandard alternative to
classical asymptotics is developed. Special emphasis is given to
applications in numerical approximation by convergent and divergent
expansions: in the latter case a clear asymptotic answer is given
to the problem of optimal approximation, which is valid for a large
class of functions including many special functions. The author's
approach is didactical. The book opens with a large introductory
chapter which can be read without much knowledge of nonstandard
analysis. Here the main features of the theory are presented via
concrete examples, with many numerical and graphic illustrations. N
General
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