Mathematical Analysis

After recapitulating the basic concepts, the first semester will provide an introduction to infinitesimal calculus with the concept of infinite succession, then pass on to elementary functions and the global study of their graph. Together with the classical functions, the course will introduce the fascinating field of parametric and polar curves. The semester will conclude with the concept of limit, which will lead to the definition of continuity and the study of the properties of continuous functions and the concept of derivative of a real function. The second semester will start with the applications of the derivative (for example problems of optimization) followed by integral calculus, with particular concern for its applications (areas, volumes, surfaces, lengths of arcs and centres of mass).