# Laurea magistrale in Economics

Servizio Studenti Internazionali

#### Corsi di studio a esaurimento

Corso a esaurimento (attivi gli anni successivi al primo)

### Mathematical models for business and economics

Codice insegnamento
4S02467
Docenti
Letizia Pellegrini, Athena Picarelli
Coordinatore
Letizia Pellegrini
crediti
6
Settore disciplinare
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
Lingua di erogazione
Inglese
Sede
VERONA
Periodo
primo semestre lauree magistrali dal 1-ott-2018 al 21-dic-2018.

## Obiettivi formativi

The main purpose of the course is to provide a range of mathematical tools in order to handle the analysis of economic phenomena. At first some basic notions on functions of several variables are recalled. Then the course provide in the 1st module, some essential knowledge on unconstrained and equality/inequality constrained optimization and, in the 2nd module, an introduction to differential equations. At the end of the course student should master the mathematical tools to solve optimization problems and differential equations that arise in the mathematical formulation of economic phenomena.

## Programma

Module 1 (prof. L. Pellegrini - 4 TC)

Functions of several variables
Level sets
Differential calculus for functions of several variables
Convex functions and generalized convexity
Unconstrained optimization
Constrained optimization with equality constraints
Lagrangian function and optimality conditions
Constrained optimization with inequality constraints
Kuhn-Tucker theorem
Constraints qualification

Module 2 (prof. A. Picarelli - 2 TC)

Ordinary differential equations: definitions, general aspects and examples
First order equations: separable equations, linear equations, phase diagram
Second order equations: linear equations with constant coefficients

A detailed program and the references to the textbooks are on the e-learning page.

Teaching supply
The course consists of 36 hours of lectures (equivalent to 6 credits).
In addition to the theoretical notions, lectures provide also some adequate set of techniques for solving exercises.

 Testi di riferimento Autore Titolo Casa editrice Anno ISBN Note C.P. SIMON, L.E. BLUME Mathematics for Economists New York, London: Norton & Company Press, Cambridge 1994 0-393-95733-0

## Modalità d'esame

Written and oral exam.
In the written test, candidates are expected to apply the fundamental notions of the course in order to solve exercises on functions of several variables, optimization problems and differential equations.
The oral exam consists at first in discussing the possible mistakes of the written test, then in investigating the theoretical competence of the candidate; hence, the knowledge of definitions and simple proofs is required.
A minimum mark is needed at the written test for the admittance to the oral discussion.

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