# Mathematical models for business and economics (2013/2014) Course code
4S02467
Name of lecturers
Letizia Pellegrini, Alberto Peretti
Coordinator
Letizia Pellegrini
Number of ECTS credits allocated
6
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
English
Period
primo semestre dal Sep 23, 2013 al Jan 10, 2014.

#### Lesson timetable

primo semestre
Day Time Type Place Note
Wednesday 2:00 PM - 4:30 PM lesson Lecture Hall C

#### Learning outcomes

The main purpose is to provide a range of mathematical tools in order to handle the economic phenomena. First of all, some basic notions on functions of several variables are recalled. Then the course aims to give, in the 1st module, some essential knowledge on unconstrained and equality/inequality constrained optimization and, in the 2nd module, an introduction to differential equations and systems of differential equations.

#### Syllabus

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

Functions of several variables
Level sets
Differential calculus for functions of several variables
Quadratic forms and definite matrices
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. Peretti - 2 TC)

A refresh on indefinite integrals and integration techniques
Ordinary differential equations. Some general aspects
Linear 1st order differential equations
Separable differential equations
Linear 2nd order differential equations. The non homogeneous case
Systems of differential equations
Linear systems. Solution by substitution
Solution of a linear system through diagonalization

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

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

 Author Title Publisher Year ISBN Note R.K. SUNDARAM A first course in Optimization Theory Cambridge ; New York : Cambridge University Press 1996 978-0-521-49770-1 C.P. SIMON, L.E. BLUME Mathematics for Economists New York, London: Norton & Company Press, Cambridge 1994 0-393-95733-0

#### Assessment methods and criteria

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 examination 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.