02541 - Mathematics for Economists

Learning outcomes

At the end of the course students are expected ti be able to apply the qualitative theory of differential and finite differences equations to the analysis of solutions of  problems in modern economic theory.

Course contents

Prerequisites

Students are expected to have a good command on the first elements of calculus, which can be achieved attending the "corso propedeutico".

 

Differential Equations

-First order ordinary differential equations: the Cauchy problem.

-Differential equation of higher order.

-Systems of ordinary differential equations. Autonomous systems and equilibria.

-Two-dimensional linear omogenenous autonomous systems. Linerarization of a non linear autonomous system in the neighbourhood of an equilibrium point.

Finite difference equations

-First order difference equations

-Systems of first order difference equations. Autonomous systems and equilibria.

-Two dimensional linear autonomous sustems. Linearization of a non linear autonomous sysyem in the neighbourhood of an equilibrium.

Introduction to dynamical optimization

-First elements of calculus of variations an optimal control and applications to some simple economic models

Readings/Bibliography

Agliardi E, Agliardi R., Matematica per la teoria economica. Pitagora

other books containing theory and examples

Marida Bertocchi, Silvana Stefani, Giovanni Zambruno, Matematica per l'economia e la finanza McGraw-Hill Company

Angelo Guerraggio - Sandro Salsa, Metodi Matematici per l'economia e le scienze sociali, G. Giappichelli Editore -Torino

Carl P. Simon, Lawrence E. Blume, Mathematics for Economists. Vol 1 & 2 W. W, Norton $ Co Inc.

Laura Recine - Maurizo Romeo, Esercizi di analisi matematica. Volume II: Funzioni di più variabili ed equazioni differenziali, Maggioli Editore.



Maurizio Romeo - Benedetto Scimmi, Esercizi di Algebra lineare e geometria, Maggioli Editore.

Problems and exescises are available in the teacher's website

Teaching methods

Lessons and exercises at the blackboard

Assessment methods

 Mandatory written test.

Optional oral exam in case of test passed.

The maximum grade achievable without oral exam is 26/30.

Teaching tools

Pencil and paper and chalk and blackboard have proved powerfully enduring and pervasive technologies in the teaching of Mathematics. When necessary the teacher exploits modern, pleasurable contexts for learning such as slides, electronic spreadsheets, projectors and the like.

Office hours

See the website of Franco Nardini