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Four examples of nonstandard reasoning in asymptotics

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

Abstract

The preceding sections illustrated the use of 7 important tools of nonstandard asymptotic analysis:

  1. 1)

    External sets and relations

  2. 2)

    Permanence principles

  3. 3)

    The classification of convex external subsets of ℝ

  4. 4)

    The lemma of dominated approximation

  5. 5)

    The concentration lemma

  6. 6)

    The Laplace method with parameters

  7. 7)

    Shadow expansions In Chapters II and III we attempt to embed the examples of this chapter into a general theory of approximation. Chapters IV, V and VI are devoted to the tools.

Keywords

  • Asymptotic Expansion
  • Small Term
  • Nonstandard Analysis
  • Taylor Polynomial
  • Order Scale

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1987 Springer-Verlag

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van den Berg, I. (1987). Four examples of nonstandard reasoning in asymptotics. In: Nonstandard Asymptotic Analysis. Lecture Notes in Mathematics, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077578

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  • DOI: https://doi.org/10.1007/BFb0077578

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17767-8

  • Online ISBN: 978-3-540-47810-2

  • eBook Packages: Springer Book Archive