MATHEMATICS, FIRST PART
The course aims to provide students with basic analytical tools to address quantitative study of economic and management subjects.
At the end of the course students will be able to
• graph elementary functions representing basic models for economic analysis;
• operate with the analytical expression of functions of one and several real variables;
• solve calculus problems with functions of one and several variables;
• solve linear algebra problems, involving matrices and vectors;
• study and solve linear systems, involving real parameters.
Lectures will discuss both theoretical arguments and solution techniques for most common exercises related to the subject. Additional exercise will be assigned during classes both for individual study and to be solved in the next lecture. Active partecipation is strongly recommended.
Main topics covered are:
Functions of one variable:
Number sets. Set R: metric structure and topology.
Real functions of real variable, domain, elementary functions, monotonicity, extreme points, concavity and convexity, geometric transformations.
Differential calculus in one variable:
Intuitive concept of derivative and its geometrical meaning. Derivatives of elementary functions. Calculus, higher order derivatives. Stationary points, test for monotonicity, convexity's test.
Functions of several variables:
Functions of two variables, domain and level curve.
Partial derivatives, stationary points. First order condition for uncostrained otpimization.
Vectors, matrices, matrix calculus and determinant, rank, linear systems.
A written exam conclude the course. Students are required to sove exercises covering all the subject presented in the classes. Exercises tests both practical and theoretical skills acquired during the course. The two hours test includes 5 multiple choice and 5 open questions.
During the teaching break and at the end of the course two partial exams will be organized, each lasting 90 minutes and covering mainly the topics of the lectures just ended. Exam is passed by achieving an average grade of 18 minimum.
Angelo Guerraggio, Matematica – Seconda edizione, Pearson, Milano, 2009.
All'inizio delle lezioni verranno indicati i riferimenti puntuali ai capitoli del testo coperti dal programma.