- Docente: Lorenzo Cerboni-Baiardi
- Credits: 6
- SSD: SECS-S/06
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Applied Economics and Markets (cod. 5969)
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from Sep 18, 2024 to Oct 23, 2024
Learning outcomes
At the end of the course the student has acquired knowledge and skills essential to the study of advanced economic systems. In particular, he/she is able to: - calculate explicitly the solution to systems of linear differential and difference equations; - study systems of nonlinear differential and difference equations; - investigating the stability of the solutions in the steady state; - detecting and studying bifurcations of equilibria.
Course contents
- Introduction
- Stock and flux variables
- Equilibria, local stability, nonlinearity
- Continuous dynamical systems
- Solutions of linear differential equations
- isoclines
- phase diagram, eigendirections
- second order differential equations
- linear approximation
- Sytems of differential equations:
- phase diagrams, fixed points, stability
- matrix notation
- solutions of homogeneous systems
- nodes, foci, saddles
- limit cycles
- Discrete dynamical systems:
- solutions of linear difference equations
- equilibria and stability
- linear difference equations of the second degree
- linear approximations
- Systems of difference equations:
- eigenvalues and eigenvectors
- solution of homogeneous systems
- trajectories
- stability and phase diagrams
- Applications to Economics
Readings/Bibliography
Economic Dynamics, Gandolfo Giancarlo, Springer-Verlag Berlin Heidelberg
Economic Dynamics Phase Diagrams and their Economic Application, Ronald Shone, Cambridge University Press
Teaching methods
lectures and exercises
Assessment methods
For the Mathematics module, the exam includes a written test on the topics covered during the course.
At free choice, the written test can be possibly integrated with a (group) project agreed with the instructor.
Evaluation judgment scale of the present module
· <18: insufficient preparation
· 18-23: sufficient preparation but relating to a limited number of the course contents;
· 24-27: adequate preparation but with some gaps with respect to the course contents;
· 28-30: very in-depth knowledge of all the course contents;
· 30L: excellent knowledge of the course contents.
Teaching tools
pdf fiiles of lectures, teacher's notes
Office hours
See the website of Lorenzo Cerboni-Baiardi