Four examples of nonstandard reasoning in asymptotics

Abstract

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

• 1) External sets and relations

• 2) Permanence principles

• 3) The classification of convex external subsets of ℝ

• 4) The lemma of dominated approximation

• 5) The concentration lemma

• 6) The Laplace method with parameters

• 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.