The course aims to provide basic knowledge of the topics of Mathematical Analysis that are the natural continuation of the contents of the course of Mathematical Analysis 1, with particular reference to differential and integral calculus in several variables. In the context of these topics, the student must be able to both know the theoretical aspects and know how to choose and use the main analytical techniques necessary for solving the proposed problems.
Course Prerequisites
Knowledge of the contents of the Mathematical Analysis 1 and Linear Algebra courses.
Teaching Methods
Frontal lessons and exercises done on the blackboard. In addition, the tutoring activity intends to offer support for the acquisition of basic manual skills regarding exercises.
Assessment Methods
The exam consists of a written test and an oral test.
The first mainly aims to verify the level of acquisition of the main analytical and calculation techniques exposed in the course, together with the ability to analyze a mathematical problem.
In the oral test (which is accessed depending on the grade obtained in the written test) an attempt is made to deepen the verification of the acquisition of the theoretical framework of reference in which the main topics covered are placed.
The written test often also contains an exercise of a more theoretical nature (usually a demonstration), which aims to verify the ability to construct a formal argument using mathematical language correctly.
Texts
The main topics are covered in the books: “Analisi matematica 1 e 2”, by C.D. Pagani and S. Salsa (Zanichelli). Analisi Matematica 2 by E. Giusti (Bollati Boringhieri)
Further reading: “Lezioni di Analisi Matematica vol. 1 e vol. 2”, by Giovanni Prodi (Bollati Boringhieri). Volume 1, in particular, contains the exposition of the concept of limit in the context of metric and topological spaces.
Some possible references for the exercises part: 'Esercizi di Analisi Matematica 2' by S. Salsa and A. Squellati (Zanichelli, 2011) "Esercizioni di Analisi Matematica Due" (first and second part) by P. Marcellini and C. Sbordone (Zanichelli, 2017)
Contents
The theoretical aspects and fundamental analytical techniques related to functions between Euclidean spaces will be considered. In particular, the following topics will be covered: metric and topological structure of Euclidean spaces; continuity, partial derivation, differentiability, gradient and Jacobian matrix; Taylor's formula and Mean Value Theorem; free and constrained extrema; implicitly defined functions and local invertibility results; Peano-Jordan measure theory, Riemann integration in several variables; reduction and change of variable theorems in multiple integrals; improper integrals; regular curves and surfaces, integration on lines and surfaces, differential forms, sequences and series of functions, pointwise and uniform convergence.
Course Language
Italian
More information
Students in the categories identified by the innovative teaching project will have the opportunity to be received by the teacher in telematic mode with times and methods to be agreed upon with the teacher; they will also be able to request access to recordings of lessons from past years.
Further information on the program and exam methods will be illustrated on the kiro page dedicated to the course.
