MATHEMATICAL ANALYSIS 2
Stampa
Enrollment year
2019/2020
Academic year
2019/2020
Regulations
DM270
Academic discipline
MAT/05 (MATHEMATICAL ANALYSIS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
Period
2nd semester (02/03/2020 - 09/06/2020)
ECTS
9
Lesson hours
84 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
VITALI ENRICO (titolare) - 9 ECTS
Prerequisites
Basic results from the courses Mathematical Analysis 1 and Linear Algebra.
Learning outcomes
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.
Course contents
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)
Teaching methods
Traditional classes.
Reccomended or required readings
'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)
Assessment methods
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.
Further information
Sustainable development goals - Agenda 2030