00679 - Mathematics

Learning outcomes

The aim of the course is to provide some basic mathematical tools needed in the study of economic and financial models, as well as prepare the students for a course in multivariate calculus with economic applications. At the end, students are expected to be familiar with the analysis of limits and differential calculus for real functions of a single real variable.

Course contents

Numerical series: geometric series, harmonic series, convergence criteria for series with non negative terms and series with terms of alternating sign.

Real functions of a single real variable: compound functions, inverse functions, graphs of inverse functions, injective and surjective functions, relations among injective, monotone and inverse functions. Limits: function's limit definitions, infinitesimal orders and infinite orders, operations with limits. Continuity of functions: definition and properties. 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's theorem, local and global extrema, necessary and sufficient conditions for local extrema, Mean-value theorem, Taylor polynomials and series, concave and convex functions, graphs of functions.

Readings/Bibliography

Metodi matematici per l'analisi economica e finanziaria, Knut Sydsaeter - Peter Hammond - Arne Strom- Pearson editore

Matematica, Angelo Guerraggio - Pearson editore

Teaching methods

Classes in presence and/or in streaming, depending on COVID-related regulations. For each topic the theoretical results will be presented: for some results a proof will be provided while for others only the underlying intuition will be given. Exercises will be solved and examined carefully in close connection with the theory. Weekly classes carried out by a tutor will be dedicated to problem solving.

Assessment methods

Assessment is based on a written exam. Exam questions involving a mixture of both calculations and reasoning are to be expected. Beyond the mechanical application of algorithms, the exam will evaluate the students' understanding of the concepts and results introduced in the course, as well as the students' ability to employ them in reasoning.

At the end of the module of Matematica Generale an intermediate exam will take place, to be completed with another partial exam at the end of the module of Matematica Applicata all'Economia. A passing grade in the integrated course of Matematica requires (i) a grade of at least 15/33 in each of the partial exams, and (ii) an average of at least 17.5/33 of the two partial grades.

All further exam calls will relate to the whole integrated course of Matematica instead of the single modules and will require a grade of at least 17.5 for passing the integrated course.

Every student is entitled to renouce a passing grade of at least 17.5 at most once.

 

Teaching tools

Electronic blackboard, IOL course page

Office hours

See the website of Iliyan Georgiev