Mathematical models for business and economics (2012/2013)

Course code
4S02467
Name of lecturers
Letizia Pellegrini, Alberto Peretti
Coordinator
Letizia Pellegrini
Number of ECTS credits allocated
6
Academic sector
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
English
Period
primo semestre dal Sep 24, 2012 al Dec 21, 2012.

Lesson timetable

Learning outcomes

The course aims to recall some basic notions on linear algebra and functions of several variables; moreover, it aims to give some essential knowledge on unconstrained and equality/inequality constrained optimization and an introduction to differential equations and systems of differential equations.

Syllabus

Module 1 (prof. L. Pellegrini)

Fundamental notions
A refresh on linear algebra.
Vector spaces and subspaces.
Systems of linear equations.
Linear transformations.

Functions of several variables
Calculus of functions of several variables.
Quadratic forms and definite matrices.
Convex functions and generalized convexity.

Optimization
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)

Differential equations
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.
Solution of a system through diagonalization.

Reference books
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

Statistics about transparency requirements (Attuazione Art. 2 del D.M. 31/10/2007, n. 544)

Data from AA 2012/2013 are not available yet