# 37292 - MATHEMATICS

### SDGs

L'insegnamento contribuisce al perseguimento degli Obiettivi di Sviluppo Sostenibile dell'Agenda 2030 dell'ONU.

## Conoscenze e abilità da conseguire

At the end of the course the students will be familiar with basic elements of mathematics that are essential for economics, statistics and econometrics comprehension. In particular, the student can afford to use linear algebra fundamentals and differential calculus elements for all the applications involved in economics, finance and management.

## Contenuti

Basic Elements
Elementary theory of real numbers. Relations and functions. Intervals, upper and lower bounds. Maximum and minimum of intervals. Algebraic, logarithmic, exponential and radical equations and disequalities. Graphic solution of equations. Analytic geometry: equations of lines, parabolas, hyperboles.

Calculus

Real functions of one real variable: properties, composition, inverse. Increasing and decreasing functions. Polynomial, logarithmic, exponential, rational and radical functions.

Limits in a real point and to infinite. Local and global continuity. Weierstrass theorem and theorem about the existence of roots for a continuous function.

Derivatives: properties and rules. Geometric meaning of the first derivative. The tangent line. Non constrained optimization: existence of maxima and minima. Concavity and convexity. Qualitative analysis of the graphs of simple functions.

Matrix and vector algebra

Introductory matrix theory and operations with matrixes. Sarrus and Laplace rules for the determinant computation of square matrixes. Properties of the determinant.

Invertible matrix, necessary and sufficient conditions for invertibility. Inverse matrix and rank.

Eigenvalues and eigenvectors of a square matrix.

Systems of linear equations: Cramer and Rouchè-Capelli theorems. Homogeneous systems. Solutions of linear systems depending on one or more parameters.

## Testi/Bibliografia

A choice between:

K. Sydsaeter, P. Hammond, A. Strom "Essential Mathematics for Economic Analysis", Pearson

S. Waner and S.R. Costenoble "Finite Mathematics and Applied Calculus"

## Metodi didattici

Lectures propose both theoretical and practical aspects concerning the different topics. Examples and exercises help students to understand the practical use of the proposed methodologies and tools.

## Modalità di verifica e valutazione dell'apprendimento

Please, check carefully the following site for the exam testing the mathematics learning requirements:

The written part of Mathematics can be organized through two partial exams, the first one in November and the second one after Christmas Holidays. When the mean score between the two parts is greater or equal to 18, then it can be the final mark. However, an elective oral examination can also be attended.

It is an open book exam.

Registration for the exam is compulsory, and students have to register through AlmaEsami, according to the general rules of the School of Economics and Management.

## Strumenti a supporto della didattica

The crash course attendance is deeply recommended. Check for the timetable in ITALI site:

http://corsi.unibo.it/1cycle/internationaltourism/Pages/default.aspx