Programme

Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.

Core Documentation

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

Type of delivery of the course

The course includes lectures and exercises. Attendance is not mandatory but strongly recommended. during the COVID-19 emergency we will follow the regulation of ’art.1 del Decreto Rettorale n°. 703 del 5 maggio 2020

Attendance

Optional

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

Programme

Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.

Core Documentation

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

Type of delivery of the course

The course includes lectures and exercises. Attendance is not mandatory but strongly recommended. During the COVID-19 emergency we will follow the regulation of ’art.1 del Decreto Rettorale n°. 703 del 5 maggio 2020

Attendance

Facoltativa

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.