Four examples of nonstandard reasoning in asymptotics

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.