- Docente: Arsen Palestini
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Economics (cod. 8408)
Learning outcomes
The aim of the course is to refresh the pre-requisite knowledge for the MATHEMATICAL ECONOMICS course, usually acquired by the student in his/her first cycle degree. At the end of the course the student has a working knowledge of: -one variable and several variable functions, static optimization, differential equations, linear algebra.
Course contents
Plan of the course:
1) Functions of 1 real variable: continuity, differentiability, derivatives, integrals, integration methods.
2) Continuous random variables: pdf, cdf, expected value and variance. Examples of different laws.
3) Ordinary Differential Equations (ODEs) and dynamical systems: equilibrium, stability, main solution methods.
4) Discrete time equations: elementary cases, steady states, applications to economic models.
5) Functions of several real variables: main definitions and properties, partial order derivatives, stationary points, Hessian matrix. Elementary surfaces in the 3-dimensional space.
6) Static optimization with and without constraints. Lagrange's multipliers method. Applications to payoff maximization and cost minimization problems.
7) Complementary topics in Mathematical Economics: implicit function theorem, Nash Equilibrium, dynamic optimization.
8) Preliminary notions of Linear Algebra: matrices, vectors, vector spaces, linear applications, rank, determinant.
9) Further topics in Linear Algebra: inverse of a non-singular matrix, symmetric matrices, quadratic forms.
10) Eigenvalues and eigenvectors of a square matrix and diagonalization.
Readings/Bibliography
Chiang, Alpha, and Kevin Wainwright. Fundamental methods of mathematical economics. McGraw-Hill, 2005.
Simon, Carl P., and Lawrence Blume. Mathematics for economists. Vol. 7. New York: Norton, 1994.
Lecture Notes of the Crash Course.
Teaching methods
The Course consists in standard traditional lectures concerning both theoretical aspects and practical examples (exercises and applications).
During the Course, some assignments will be possibly proposed to the students to augment their knowledge and enhance their abilities.
Assessment methods
No final test is required.
During the Course, the teacher intends to provide the students with some helpful tools for self-assessment.
Office hours
See the website of Arsen Palestini