Catalogo dei Corsi di studio

The goals consist of a good knowledge of the terminology adopted in the context of Mathematical Analysis.

It is expected that the students will be familiar with the proof techniques, they will have a knowledge of the fundamentals about sequences and serie of functions, Taylor Series, Fourier Series, functions of n real variables, integrals in R^2, R^3, curve, line integrals. differential forms, vector fields, surfaces and integration, complex functions, holomorphy, integration in C, antiderivatives, analytic functions, zeroes and singularities. Laurent series, Laplace Transform.

Crucial achievements are the ability in applying theorems and concepts learned during the course, in developing strategies and methods to solve problems. It is expected to be able to share and communicate information about the topics of the course with a correct formal language, dominating the contents, computing integrals in R^2, R^3, along curves, in the complex plane, along surfaces; making estimates in term of series, detecting critical points of functions of n real variables, expanding regular functions in power series, and periodic ones in Fourier series, solving improper integrals by means of residues, compute Laplace transform and its inverse in basic cases.

It is important to detect the more effective and efficient method for problem solving, also in a way to apply the knowledge to different frameworks than the pure mathematical one.

The learners are expected also to be able to deepen the contents, consulting and using materials other than those offered during the course. It is important the adoption a scientific approach based on the formal evidence and rigorous proofs, devoted to clarify questions also in order to improve general understanding of phenomena.

Programme

Functions of more real varaibles. Topology and differential calculus in R^2 and R^3. Critical points. Integration in R^2, R^3. Curves. Vector fields, differential forms. Line integrals. Surfaces.
Sequences and series of real functions. Power series. Taylor Series. Fourier Series.
Complex Analysis. Differential calculus in C. Integration in C. Holomorphy. Series. Power series. Analytic functions. Singularities. Laurent Series. Residues and application.
Laplace transfor,m: properties, calculus. Inversion of Laplace transform.

Adopted texts

Esercizi di Analisi Matematica II in campo reale e complesso
Casalvieri-De Cicco
La Dotta

For a deeper learning and more contents:

Lezioni di Analisi Matematica II
Nicola Fusco, Paolo Marcellini, Carlo Sbordone
Zanichelli

Matematica per l'Ingegneria dell'Informazione or Metodi matematici per l'ingegneria
Giulio Cesare Barozzi Codegone-Lussardi
Zanichelli Zanichelli

Analisi Matematica II
Micol Amar, Alberto Maria Bersani
Edizioni La Dotta

Metodi Matematici per l'Ingegneria
Virginia De Cicco, Daniela Giachetti
Soc. Editrice Esculapio

Materiale didattico aggiuntivo verrà fornito durante il corso.

Prerequisites

The exam can be given after having passed Mathematical Analysis I. I suggest the students to have a good knowledge of Geometry and Linear Algebra.

Study modes

Lectures will be given in class.

Frequency modes

It is reccomended to attend the lectures either in person or from remote

Exam modes

The exam consists of a written text with both multiple choice questions and problems. For those who want to improve their grades (>28) or for those who do not reach the minimum (i.e. grades between 15 and 17) it is possible to ask for an oral exam.

During and at the end of the course it is possible to have from 1 to 3 preliminary tests (each one representing 1/3 of the exam) with both the multiple choice questions and the open ones. The third test will be given at the end of the course.

Exam reservation date start	Exam reservation date end	Exam date
07/01/2021	07/02/2022	15/02/2022
07/01/2021	07/02/2022	15/02/2022
23/02/2022	15/03/2022	30/03/2022
23/02/2022	15/03/2022	30/03/2022
10/05/2021	14/06/2022	15/06/2022
10/05/2021	14/06/2022	15/06/2022
07/06/2021	07/07/2022	18/07/2022
07/06/2021	07/07/2022	18/07/2022
07/07/2021	11/09/2022	19/09/2022
07/07/2021	11/09/2022	19/09/2022
23/09/2022	07/10/2022	12/10/2022
23/09/2022	07/10/2022	12/10/2022
10/11/2022	09/01/2023	18/01/2023
10/11/2022	09/01/2023	18/01/2023

Programme

Functions of more real varaibles. Topology and differential calculus in R^2 and R^3. Critical points. Integration in R^2, R^3. Curves. Vector fields, differential forms. Line integrals. Surfaces.
Sequences and series of real functions. Power series. Taylor Series. Fourier Series.
Complex Analysis. Differential calculus in C. Integration in C. Holomorphy. Series. Power series. Analytic functions. Singularities. Laurent Series. Residues and application.
Laplace transfor,m: properties, calculus. Inversion of Laplace transform.

Adopted texts

Esercizi di Analisi Matematica II in campo reale e complesso
Casalvieri-De Cicco
La Dotta

For a deeper learning and more contents: Lezioni di Analisi Matematica II
Nicola Fusco, Paolo Marcellini, Carlo Sbordone
Zanichelli

Matematica per l'Ingegneria dell'Informazione
Giulio Cesare Barozzi
Zanichelli
(or Metodi matematici per l'ingegneria
Codegone-Lussardi
Zanichelli)

Analisi Matematica II
Micol Amar, Alberto Maria Bersani
Edizioni La Dotta

Metodi Matematici per l'Ingegneria
Virginia De Cicco, Daniela Giachetti
Soc. Editrice Esculapio

Some notes will be provided during the course.

Prerequisites

The exam can be given after having passed Mathematical Analysis I. I suggest the students to have a good knowledge of Geometry and Linear Algebra.

Study modes

The course will be offered in person.

Frequency modes

it is reccomended to attend the lectures in presence or from remote, according to University's rules.

Exam modes

The exam consists of a written text with both multiple choice questions and problems. For those who want to improve their grades (>27 or between 15 and 17) it is possible to ask for an oral exam.

During and at the end of the course it is possible to have from 1 to 3 preliminary tests (each one representing 1/3 of the exam) with both the multiple choice questions and the open ones. The third test will be given at the end of the course.

Exam reservation date start	Exam reservation date end	Exam date
07/01/2021	07/02/2022	15/02/2022
07/01/2021	07/02/2022	15/02/2022
23/02/2022	15/03/2022	30/03/2022
23/02/2022	15/03/2022	30/03/2022
10/05/2021	14/06/2022	15/06/2022
10/05/2021	14/06/2022	15/06/2022
07/06/2021	07/07/2022	18/07/2022
07/06/2021	07/07/2022	18/07/2022
07/07/2021	11/09/2022	19/09/2022
07/07/2021	11/09/2022	19/09/2022
23/09/2022	07/10/2022	12/10/2022
23/09/2022	07/10/2022	12/10/2022
10/11/2022	09/01/2023	18/01/2023
10/11/2022	09/01/2023	18/01/2023