# 16954 - Mathematics 2

## Learning outcomes

At the end of this course, the student has the basic knowledge of the differential and integral calculus for functions of several real variables. He knows the most elementary methods for the resolution of differential equations, and the fundaments of linear algebra. In particular, he knows how to compute determinants of matrices, how to solve linear systems of equations, how to apply differential and integral calculus for for functions of several real variables.

## Course contents

Points and vectors in 2, 3 or more dimensions. Vector spaces, linear independence, basis. Linear transformations, matrices. Eigenvalues and eigenvectors of matrices. Diagonalization. Functions of 2 or more variables: limits, continuity, partial derivatives. Differentiability. Gradient, directional derivatives, critical points, Hessian. Taylor formula of second order. Notions of differential calculus in several variables. Multiple integrals.

- M. Bramanti, C. D. Pagani, S. Salsa, "Matematica: calcolo infinitesimale e algebra lineare", 2a ed., Zanichelli, 2004
- S. Salsa, A. Squellati, "Esercizi di matematica 1: calcolo infinitesimale e algebra lineare", Zanichelli, 2001
- S. Salsa, A. Squellati, "Esercizi di matematica 2: calcolo infinitesimale", Zanichelli, 2002

## Teaching methods

Matematica 2 (6 ects) is a second semester course and represents the second part of the integrated course Matematica (15 ects). The first part (Matematica 2, 6 ects) and the third part (Complementi di Matematica, 3 ects) are held by Prof. Emanuela Caliceti (first semester) and Dr. Emanuele Mingione (second semester), respectively.

The part Matematica 2 consists of classroom lectures where, first of all, the theoretical aspects of each topic are illustrated. More precisely, after introducing the basic elements, then the main theorems and results are stated and, in some cases, proved. Afterwards, several lectures are devoted to the applications of the notions and techniques previously introduced, and to solving exercises and problems.

## Assessment methods

For the part Matematica 2 the assessment method consists, together with Complementi di Matematici, in a final written test of 3 hours and a half(use of books, lecture notes, electronic devices not allowed). The test is structured in two parts: the first part consists of exercises on Matematica 2 to be solved, with a score out of 20's. The second part consists of exercises on Complementi di Matematici to be solved, with a score out of 10's.

In order to pass the test students must obtain a score larger or equal to 16 for the first part, and to 6 for the second part.

The final score relative to the whole integrated course Matematica is the weighted mean (based on the ects) of the scores obtained in the two test of Matematica 1 (6 ects)and the (joint) test of Matematics 2 and Complementi di Matematica (9 ects). To register the score students must sign up through Almaesami and attend one of the dedicated sessions.

## Office hours

See the website of André Georges Martinez