00679 - Mathematics

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 study functions 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. Differential calculus: definition of first derivative, geometric meaning, tangent straight line equation to the graph of a differentiable function operations with derivatives; De l'Hopital theorem, local and global extremes, necessary and sufficient conditions for local extremes,  Lagrange theorem, , Taylor's polynomial, concave and convex functions, graphs of functions.
Numerical series:  geometric series,  harmonic series, convergence criteria for series with non negative terms and series with alternating sign. 

 

Readings/Bibliography

Teacher's Lecture Notes downloadable from the University web site

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

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

 

 

Teaching methods

Classes. For each topic the theoretical results will be presented: for some of them the proof will be provided while for the others only the underlying intuition. Exercises will be solved and examined carefully. Weekly classes taken by the tutor will be devoted to the solution of exercises. 

Assessment methods

The assessment method consists in two steps:
1) a preliminary test with 6 questions: each correct answer worth 3 points, each wrong answer -1 point while answers not given are not considered (their value is 0). A final score of 10 points is required to be admitted to the second step.
2) a written exam with questions to be solved in details.  The final grade is the weighted average of the achieved grades.
The final grade of the integrated course of "Matematica" (12 cfu)  is the arithmetic mean of the grades obtained in the two modulus (Matematica Generale and Matematica per l'Economia) if a grade of at least 14 points is achieved in each exam.
The oral exam is optional but it is required a mean score of at least 18 points: in case of lower average scores, the admission is at professor's discretion .

Teaching tools

None

Office hours

See the website of Sabrina Mulinacci