Università Roma Tre

Axioms of reals (included inductive definition of N, archimedean property, density of rationals).
Limit theory for real-valued functions of one real variable (included series and sequences).
Topology and sequences.
Continuous and uniformly continuous functions: fundamental theorems; main topological invariants.
Note: a significative part pf the course is devoted to the rigorous definition and to the properties
of the fundamental analytic functions (roots, exponentials, logarithms, hyperbolic and trigonometric functions and theor inverse functions).

Luigi Chierchia AnalisiMatematica.1, Una introduzione rigorosa all'analisi matematica su R; Parte 1 - Dispense AA 2018-2019 ( Libreria Efesto )