Catalogo dei Corsi di studio

The main purpose of the course is to give the student a good knowledge of the basic theory of Differential and Integral Calculus of Functions of several variables, as well as of Linear Algebra.

Specific objectives :

Knowledge and understanding: at the end of the course the student will have learned the basic theory to study functions of several variables both with scalar or vector values. Moreover he/she will be able to study simple linear maps between vector spaces.

Applications : at the end of the course the student will be able to solve simple problems which require the use of the differential and integral calculus . In particular he /she will be able to find extremals of functions of several variables and also determine the potential of a vector field. Moreover he/she will have the ability to solve linear systems.

Critical abilities: the student will have the basic knowledge to understand the mathematical tools necessary to study Chemistry and Physics and the way to derive some formulas used in these fields.

Communication skills: the student will have the ability to expose the topics studied in written and in oral form.

Learning skills: the course will improve the logical abilities and of learning of various scientific disciplines.

Exam reservation date start	Exam reservation date end	Exam date
22/02/2021	11/06/2021	15/06/2021
15/06/2021	01/07/2021	05/07/2021
30/07/2021	03/09/2021	06/09/2021
04/09/2021	13/09/2021	15/09/2021
30/09/2021	08/01/2022	11/01/2022

Programme

Linear Algebra : Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems - Quadratic forms.

Functions of several variables : Limit and continuity - Partial and directional derivatives and differentiability- Higher derivatives , Taylor formula - Local and global maxima or minima.

Vector valued functions : Regular curves and their length - Integral on curves - Vector fields and their integral on curves - Conservative vector fields.

Integral for functions of several variables : Integrals on planar domains, triple integrals- Recduction and change of variables formulas - Gauss Green and Divergence theorems.

Adopted texts

- Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli

Bibliography

Salsa S., Squellati A. Esercizi di Analisi Matematica 1/2

Prerequisites

Differential calculus and integrals for functions of one variable.

Frequency modes

Attendance of lessons is not compulsory

Exam modes

The written exam consists of both exercises and questions concerning the theory. There are two intermediate checkpoints, which can substitute the written exam.
An oral exam could be requested and is necessary to obtain full marks evaluation.

Exam reservation date start	Exam reservation date end	Exam date
25/05/2021	13/06/2021	15/06/2021
25/06/2021	08/07/2021	12/07/2021
20/08/2021	01/09/2021	06/09/2021
20/08/2021	10/09/2021	15/09/2021
25/12/2021	15/01/2022	20/01/2022

Programme

Linear Algebra : Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems - Quadratic forms.

Functions of several variables : Limit and continuity - Partial and directional derivatives and differentiability- Higher derivatives , Taylor formula - Local and global maxima or minima.

Vector valued functions : Regular curves and their length - Integral on curves - Vector fields and their integral on curves - Conservative vector fields.

Integral for functions of several variables : Integrals on planar domains, triple integrals- Recduction and change of variables formulas - Gauss Green and Divergence theorems.

Adopted texts

- Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli

Prerequisites

Differential and integral calculus for functions of one variable.

Exam modes

The evaluation is based on a written and oral exam. The last one can be granted depending on the result of the written part.

Programme

Linear Algebra:
Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems

Functions of several variables:
Limits and continuity - Partial and directional derivatives - Differentiability - Higher order derivatives - Local and global maxima or minima

Vector valued functions:
Regular curves and their length - Integrals on curves - Vector fields and their integral on curves - Work done by a field along a curve - Conservative vector fields

Integrals for functions of several variables:
Integrals on planar domains - Triple integrals - Reduction and change of variables formulas - Gauss Green and Divergence theorems

Adopted texts

Bramanti-Pagani-Salsa "Analisi matematica 2"

Prerequisites

Differential calculus for functions of 1 real variable: Notions of limit, sequence, continuity, derivative, Riemann's integral.

Exam modes

The oral exam is optional, unless the score of the written exam is lower than 21.
Maximal score without the oral exam = 27.

Exam reservation date start	Exam reservation date end	Exam date
08/05/2021	14/06/2021	15/06/2021
18/05/2021	21/06/2021	22/06/2021
22/06/2021	04/07/2021	05/07/2021
30/06/2021	07/07/2021	08/07/2021
15/08/2021	04/09/2021	06/09/2021
09/09/2021	13/09/2021	15/09/2021
25/12/2021	12/01/2022	19/01/2022

Programme

Linear Algebra : Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems - Quadratic forms.

Functions of several variables : Limit and continuity - Partial and directional derivatives and differentiability- Higher derivatives , Taylor formula - Local and global maxima or minima.

Vector valued functions : Regular curves and their length - Integral on curves - Vector fields and their integral on curves - Conservative vector fields.

Integral for functions of several variables : Integrals on planar domains, triple integrals- Recduction and change of variables formulas - Gauss Green and Divergence theorems.

Adopted texts

- Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli

Bibliography

P. Marcellini, C.Sbordone , Esercitazioni di Matematica - II volume, parte prima e seconda.

Prerequisites

Differential calculus and integrals for functions of one variable.

Frequency modes

It is advisable to take the classes.

Exam modes

The evaluation is based on a written and oral exam. The last one can be granted depending on the result of the written part. The written exam can be substituted by two intermediate partial exams given after the first half of the course and after the end of the course.

Exam reservation date start	Exam reservation date end	Exam date
24/05/2021	10/06/2021	15/06/2021
25/06/2021	08/07/2021	12/07/2021
20/08/2021	01/09/2021	06/09/2021
20/08/2021	10/09/2021	15/09/2021
02/11/2021	12/11/2021	18/11/2021
27/12/2021	16/01/2022	20/01/2022