Multidimensional differential and integral calculus. Introduction to Lebesgue measure and Lebesgue integral. Combinatorial problems. Elementary probability. Discrete random variables. Gaussian distribution.
1. G.Giaquinta, G.Modica, Analisi Matematica IV, Funzioni di più variabili. Pitagora, 2005.
2. G.Modica , L.Poggiolini. Note di Calcolo delle Probabilità, Pitagora, 2011.
Learning Objectives
The ourse has a goal providing students with
KNOWLEDGE about elements of calculus for functions of several variables: partial derivatives, gradient, multiple integrals, Lebesgue measure, area and volumes. Enumeration problems, basic probability, discrete and absolutely continuous random variables.
EXPERTISE necessary for construction and analysis of mathematical models, which are based on multivariable calculus. One gains expertise in resolution of combiantorial problems. We teach fundamentals of probability theory so that students will be capable to develop and analize basic probabilistic models.
Prerequisites
Differential and integral calculus for the functions of real variable
Teaching Methods
Lectures: presentation of the theory contained in the program of the course, with direct interaction between student and teacher, to ensure comprehension of the contents.
Moodle online learning platform: online teacher-student interaction, allocation of lists of exercises, bibliographic references, written tests from previous years.
Type of Assessment
Two intermediate written tests which contain 7-8 theoretic questions anmd exercises. Final oral examination which evaluates the capacity of understanding and presenting the theoretical contents, as well as originality and autonomy of reasoning.