Elementi di analisi matematica

This text is aimed at all students of scientific disciplines who wish to familiarize themselves with the concepts and methods of analysis, acquiring sufficient knowledge and skill for the needs of their degree courses. The aim was therefore always to adopt the simplest possible situation, sacrificing generality in favor of immediacy and simplicity, without however ever renouncing the rigor of demonstrations, which is the essential characteristic of mathematical discourse at any level.

When possible, the choice was made among the various demonstrations that seemed most consistent with intuition, even if there were shorter ones but less expressive. When then, on some rare occasions, the complexity of the demonstration would have required too much space, it was preferred to leave it out altogether in order not to weigh down the discourse beyond what is appropriate. In the choice of topics, the tradition of one-variable analysis courses has been followed; a chapter dedicated to elements of analytical geometry and another on differential equations has been added, which are usually found in later courses.

The result is a volume that may be slightly larger than can be contained in a university course. However, it was not wished to renounce a certain completeness, leaving the teacher to neglect some parts (and perhaps expand others) according to the needs of his course.