MATHEMATICAL ANALYSIS D
Learning outcomes of the course unit
Touch some subjects not included in elementary courses.
Recover (in part) the mind-shaping value of the scientific method, by giving a detailed proof of every assertion.
Analisi matematica AB, Analisi matematica C, Geometria
Course contents summary
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.