Stratified analysis?

Abstract

It is now over forty years since Abraham Robinson realized that the concepts and methods of Mathematical Logic are capable of providing a suitable framework fur the development of the Differential and Integral Calculus by means of infinitely small and infinitely large numbers (Robinson [29], Introduction, p. 2). The magnitude of Robinson's achievement cannot be overstated. Not only does his framework allow rigorous paraphrases of many arguments of Leibniz, Euler and other mathematicians from the classical period of calculus; it has enabled the development of entirely new, important mathematical techniques and constructs not anticipated by the classics. Researchers working with the methods of nonstandard analysis have discovered new significant results in diverse areas of pure and applied mathematics, from number theory to mathematical physics and economics. © 2007 Springer-Verlag Wien.