Mathematical models for business and economics (2019/2020)

Learning outcomes

The main purpose of the course is to provide a range of mathematical tools to handle the analysis of economic problems. At first, some basic notions on functions of several variables are recalled. Then, in the first module, the course provides some essential knowledge on unconstrained and equality/inequality constrained optimization. In the second module, ordinary differential are introduced;  solutions for separable and linear first order equations  are discussed. At the end of the course students should master the mathematical tools to solve optimization problems and differential equations arising from the mathematical formulation of economic phenomena.

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. 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.

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.