Argomenti dell'insegnamento
• Sequences and series: definitions and basic properties of sequences and series of real numbers. • Univariate functions: definitions and basic properties of real functions in one variable, limits, continuity. • Derivatives and differentials: definitions and main theorems of differential calculus. • Indefinite and Riemann integrals: definitions and main theorems of integral calculus. • Basic optimization techniques in one variable: study of functions, local and global extrema, first and second derivative tests, standard form of optimization problems, Taylor polynomials, Newton's method. • Mathematical tools for decision making without and with uncertainty: sets and relations, principle of mathematical induction, basics of Combinatorics, Newton's Binomial Theorem, Pascal's Triangle, hints on Multivariate Calculus and applications.

Modalità di insegnamento
• Frontal classroom lectures • Lab exercises In the lectures, concepts and techniques are introduced, both by presenting notions on the blackboard and by collectively discussing related exercises and examples. In the labs, students (either in small groups, or individually) develop possible approaches to address the exercises proposed by the lecturer and compare their solutions with the rest of the class.

Obiettivi formativi
The course belongs to the type "di base – formazione matematico-fisica". The course offers an introduction to the fundamental concepts and techniques of elementary calculus, mathematical analysis and optimization in connection to their use in business informatics and economics. Knowledge and understanding: • D1.1 - Possess basic knowledge of mathematical analysis, algebra, numerical calculation and optimisation methods which support computer science and advanced economics. Applying knowledge and understanding: • D2.1 - Ability to use mathematics and statistical data analysis tools to solve computational problems. Learning skills • D5.1 - Learning ability to undertake further studies with a high degree of autonomy.

Modalità d'esame
The final exam consists of a written test (50%) and an oral test (50%). The written test (of 2 hours) contains questions and exercises on the material covered during the course. The oral test (of ca. 20 minutes) can involve both a discussion of the answers given in the written part, as well as unseen questions and short exercises based on the course topics. The aim of both the written and the oral tests is to check to which degree students have mastered the following learning outcomes: 1) acquiring knowledge and understanding; 2) applying knowledge and understanding.

Criteri di valutazione
Correctness and clarity of the answers.