From Peano's axioms to the real numbers; induction; sequences; construction of the exponential function. Sequences defined recursively (dynamical systems). Metric spaces; sequences of functions. Differential equations: existence, uniqueness, comparison and extension theorems, maximal existence, qualitative behaviour.
E. Acerbi, G. Buttazzo: Primo corso di analisi matematica, Pitagora 1999. Some notes will be handed out on specific subjects.