Name: nonstandard asymptotic analysis
SKU: 3483998
Price: 1085.00 TWD
Availability: InStock
Author: berg
ISBN: 9783540177678

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Type

Physical Book

Publisher

Springer

Author

berg

Language

English

Pages

187

ISBN

3540177671

ISBN13

9783540177678

Synopsis "nonstandard asymptotic analysis"

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 authors 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