00679 - Mathematics

Academic Year 2010/2011

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Economics, Markets and Institutions (cod. 8038)

Learning outcomes

The aim of course is to provide the mathematical tools needed to study economic and financial models. At the end, students are required to be able: to solve any linear system, to compute integrals and to study function of real variables.

Course contents

-Real function of a real variable: domain and image, asymptotic straight lines, elementary functions, compound functions, inverse function, inverse functions graphs, injective and surjective functions, relations among injective, monotone and inverse functions.
- Limits: function's limit definitions, infinitesimal order and infinite order, operations with limits.
- Continuous functions: definition, elementary continuous functions, discontinuity points, theorems on continuous functions: Weierstrass theorem, theorems on the continuity of the inverse function and the compound function.
- Differential calculus: definition of first derivative, geometric meaning, tangent straight line equation to the graph of a differentiable function, differentiability and continuity relation, operations with derivatives; De l'Hopital theorem, local and global extremes, necessary and sufficient conditions for local extremes, Fermat's theorem, Lagrange theorem, concave and convex functions, graphs of functions, Taylor polynomial.
Functions of several variables: domain, indifference curves, limits and continuity, local and global extremes, differential calculus (partial derivatives, first and second order differential) , implicit functions, Taylor formula of the II order, free extremes computation, cancave and convex functions, constrained extremes (Lagrange multipliers method).

Readings/Bibliography

Peccati-Salsa-Squellati, Matematica per l'Economia e l'Azienda, EGEA, Milano, 1999

Scaglianti-Torriero, Matematica metodi e applicazioni, CEDAM, Padova, 2002

Notes provided by the teacher.

Teaching methods

Classes on blackboard. Classes in which students are called to actively participate are scheduled.

Assessment methods

A written test with both exercises and questions. The oral exam is optional. At the end of the course a test is scheduled.

Office hours

See the website of Sabrina Mulinacci