Nonstandard Asymptotic Analysis

  • Authors
  • Imme van den Berg

Part of the Lecture Notes in Mathematics book series (LNM, volume 1249)

About this book

Introduction

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

Keywords

DEX Lemma approximation behavior boundary element method calculus class form function functions knowledge sets special function

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0077577
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17767-8
  • Online ISBN 978-3-540-47810-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book