Programme

Number sets (N, Z, Q and R), axiomatic construction of R, construction of N and the inductive method, complex numbers; topological concepts in R and Bolzano-Weierstrass theorem; real functions with a real variable, limits for functions and properties, limits for sequences, special limits, the Napier number; continuous functions and their properties, fundamental theorems on continuous functions (zeroes, intermediate values, Weierstrass); derivative of a function and properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex/concave functions; graph of a function; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, change of variables and integration by parts, intergation rules; numerical series and convergence, simple and absolute convergence, convergence criteria for positive series and for general series; Taylor series; improper integrals.

Core Documentation

Analisi matematica I Marcellini-Sbordone
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone

Attendance

Attendance is not mandatory but strongly recommended.

Type of evaluation

The written exam is aimed at evaluating the student's ability to perform exercises also of a theoretical nature. It lasts two hours and consists of a first part with four multiple choice questions and a second part with an open question. The student can be exempted from the written exam if he passes an intermediate written test on the first part of the course and a final one on the second part of the course, each lasting two hours, structured in a similar way to what is described above. In the first session, the student will have the opportunity to recover one of the two intermediate tests. After passing the written examination, there is an oral discussion which is relevant for the grade attribution