V. Functions of Two Variables

Abstract

A quick review of the structure so far exposed of the lecture course shows that both in treating the variables x and the functions of one variable f(x) we always had to stress the contrast between approximation and precision mathematics. The various practical applications of mathematics were then linked to approximation mathematics. Geometry lies, in a manner of speaking, in the middle. Here we are using geometry mainly to facilitate the understanding of abstract considerations. The matter is as follows: Insofar as we treat curves that we can draw and imagine concretely we primarily explain relations of approximation mathematics; on the other hand, this geometric representation allows us to refer to the ideal object and thus to indirectly clarify its meaning, like – for instance – we clarified the essence ofWeierstraß function by considering the successive approximating curves.