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

Prerequisites: Knowledge of the topics covered in the first module, Mathematics 1, is required.

Syllabus:

Linear algebra: Ordered pairs, triples, and n-tuples; points and vectors. Vector spaces, linear dependence and independence, bases. Linear transformations, matrices. Eigenvalues and eigenvectors. Diagonalization of matrices.

Functions of two or more variables: Limits, continuity, partial derivatives. Differentiability. Gradient, directional derivatives, critical points, Hessian matrix. Second-order Taylor expansion. Fundamentals of multivariable differential calculus. Multiple integrals.

Differential equations: Complex numbers, first-order and second-order linear differential equations.

Readings/Bibliography

- 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 (12 ects).  

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

The learning assessment for the Mathematics 2 part consists  in a written test with a duration of  3 and a half hours. The test will contain exercises to solve and theoretical questions. The use of: books, notes, calculators, computers is not permitted. The grade for the exam of the entire integrated Mathematics course is calculated as the average of the grades obtained in the Mathematics 1 test (6 cfu) and in the Mathematics 2 test (6 cfu).

 

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

Teaching resource online platform Virtuale

Office hours

See the website of Emanuele Mingione

See the website of Federica Gerace