- Docente: Sabrina Mulinacci
- Credits: 5
- SSD: SECS-S/06
- Language: Italian
- 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 requiredto befamiliar with the analysis of limits and differential calculus.
Course contents
Real function of a real variable: 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 that can be downloaded from the University web site
Bibliografia:
A. Ambrosetti, I. Musu, Matematica generale e applicazioni all'economia, Liguori.
Bergamini, Ritelli, Trifone: Fondamenti di Matematica, Zanichelli, Bologna, 2005.
Guerraggio, Matematica, Pearson-prentice-Hall (2a ed.)
Peccati-Salsa-Squellati, Matematica per l'Economia e l'Azienda, EGEA, Milano
Ricci, Matematica Generale, McGraw-Hill
Scaglianti-Torriero, Matematica metodi e applicazioni, CEDAM, Padova
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 oral exam is optional but it is required a mean score of at least 18/30: in case of lower average scores, the admission is at professor's discretion .
The minimum score is 15/30 and the final grade of the integrated course of "Matematica" (11 cfu) is the weighted average of the grades obtained in the two modulus (Matematica Generale and Matematica per l'Economia).
Teaching tools
Blackboard
Office hours
See the website of Sabrina Mulinacci