Professor
Chiara GiacomoniLearning outcomes
The course aims to provide tools for achieving a proper knowledge of the basic concepts of mathematical analysis and linear algebra and to develop and strengthen calculation skills. Particular attention is focused on the choice of examples, sometimes chosen from applied sciences, or from more common applications, in order to stimulate logical-deductive attitudes.
Expected learning outcomes
Students should be able to understand and apply the concepts of algebra and functions to solve problems related to geometry and construction.
Course contents
Main topics: basic notions of set theory; introduction to logic; real numbers, completeness axiom; complex numbers; elements of topology, accumulation points, Bolzano-Weierstrass theorem, Cantor theorem; elementary functions, function behaviour, interpretation of graphs, injectivity, surjectivity, bijectivity, inverse, increasing and decreasing function, composite function, monotonic functions; the limit of a function, properties of the limit, continuity of a function, Weierstass theorem, intermediate value theorem, discontinuities; derivatives, analytic and geometric notions of derivative, fundamental theorems on differential calculus, Fermat theorem, Rolle theorem, Lagrange theorem, applications of derivatives, inflection points, asymptotes; local and global extrema; Riemann integral, sufficient and necessary conditions for the existence of Riemann integral, integration by parts and change of variable, fundamental theorem of integral calculus. Linear algebra: matrices, determinant, rank, linear systems.
Prerequisites
Basic mathematical knowledge acquired from high school, such as algebraic equations and inequalities of first and second order, power, exponential, logarithmic and trigonometric functions. These topics are resumed in the pre course that is held every year before the beginning of the course.
Reading/Bibliography
Teacher’s notes: - Analisi Matematica di Bertsch, Dal Passo, Giacomelli – Mcgraw-Hill - Esercitazioni di Matematica - XNUMX° volume parte prima – P. Marcellini, C. Sbordone – Liguori Editore - Esercitazioni di Matematica - XNUMX° volume parte seconda – P. Marcellini, C. Sbordone – Liguori Editore
Teaching methods
Lectures in the classroom and exercises carried out with the aid of computer projections.
Assessment methods
The exam consists of two parts, written (2 or 3 hours) and oral (40 minutes). Admission to the oral test is allowed only to who already passed the written test.