2019/2020

2019/2020

DM270

MAT/05 (MATHEMATICAL ANALYSIS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

2nd semester (02/03/2020 - 09/06/2020)

9

84 lesson hours

Italian

WRITTEN AND ORAL TEST

VITALI ENRICO (titolare) - 9 ECTS

Basic results from the courses Mathematical Analysis 1 and Linear Algebra.

The principal aim is to lead students to master the basic elements in the fields of Mathematical Analysis which are the natural continuation of the contents of the course Mathematical Analysis 1. Within these areas the student will be expected to know the main theoretical features and to be able to suitably select and apply the principal techniques from Analysis for the resolution of the proposed problems.

The course will focus on the theoretical fundamentals and the key analytical techniques related to the study of functions between Euclidean spaces. In particular, the foolowing topics will be dealt with. Partial derivatives, differential, gradient and Jacobian matrix. Taylor formula and the Mean Value Theorem. Maxima and minima with and without constraints. Implicit functions and local invertibility results.
Peano-Jordan measure and Riemann integral. Fubini’s Theorem. Change of variables in multiple integrals.
Regular manifolds in Euclidean spaces. Integration on a manifold. Differential forms.
Basic results on numerical series.

Notice: the program written above will be reduced for students from "Complementi di analisi matematica 1" (Laurea in Fisica)

Traditional classes.

'Lezioni di analisi matematica' vol.2 by Giovanni Prodi (Boringhieri)

'Analisi matematica 2' by Carlo D. Pagani and Sandro Salsa (Zanichelli)

'Esercizi di Analisi Matematica 2' by Sandro Salsa and Annamaria Squellati (Zanichelli, 2011)

The exam consists in a written test and in an oral part. The first one mainly aims to check the level of knowledge of the principal analytical methods dealt with in the course, together with the ability to face a mathematical problem in the field. A threshold mark is needed to pass to the oral part, which intends to verify the global understanding of the theoretical framework.