Learning objectives
<br /><br />Touch some subjects not included in elementary courses. <br />Recover (in part) the mind-shaping value of the scientific method, by giving a detailed proof of every assertion.
Prerequisites
Analisi matematica AB, Analisi matematica C, Geometria
Course unit content
<br /><br />From Peano's axioms to the real numbers; induction; sequences; construction of the exponential function. <br />Sequences defined recursively (dynamical systems). <br />Metric spaces; sequences of functions. <br />Differential equations: existence, uniqueness, comparison and extension theorems, maximal existence, qualitative behaviour.
Full programme
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Bibliography
<br /><br />E. Acerbi, G. Buttazzo: Primo corso di analisi matematica, Pitagora 1999.<br />Some notes will be handed out on specific subjects.
Teaching methods
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Assessment methods and criteria
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Other information
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