Mathematical Analysis 2

The course is devoted to carry on the illustration of basic concepts of Mathematical Analysis, previously started with the course of Mathematical Analysis 1. That is done not bounding the teaching to the calculus techniques, but opening it to an incisive learning. Mean objects are Riemann integration theory for functions of one real variable, differential calculus for functions of several real variables with application to free optimization, study of sequences and series of functions and basic background on ordinary differential equations together with related integration techniques.

We expect the student to absorb the fully basic notions, that have been taught, at the suitably incisive level relatively to his scholarship, taking into account that the given one is a course in Mathematical Analysis, not simply in Calculus. Assume the student will had taken successfully the course: not only he will get a suitable manual skill in calculus, but he will be also able to deal with problems, in the context of the taught subjects, that, even set in stabilized models, cannot be solved by a passive application of standard rules. In particular:
· when dealing with the integration of ordinary differential equations or the free optimization, he will be able to get suitable estimates when the exact results are not available or not requested;
· he will be able to manage the limit processes for sequences of functions with respect to the most significant properties of regularity.