37292 - MATHEMATICS

Conoscenze e abilità da conseguire

The course aims at giving the student a basic knowledge of differential and integral calculus, and linear algebra for the study of economics, financel and statistical analysis. By the end of the course students have the ability to perform basic operations with vectors and matrices, to compute determinants, and to solve linear systems. As far as calculus is concerned, they can apply the methods of differential and integral calculus to plot the graph of functions, to compute the area of plane domains, and to find and classify critical points of functions of two variables.

Contenuti

A Crash course covers a number of introductory topics (so-called precalculus), including elementary set theory, sets of real numbers, polynomials, linear and quadratic equations and inequalities, systems of inequalities, absolute value and rational inequalities, exponential and logarithmic equations and inequalities, Cartesian coordinate system, basic analytic geometry.

NOTE: A perfect knowledge of the Crash course contents is of vital importance to understand the more advanced topics of the course of Mathematics.

Course content -Mathematics

Linear Algebra

Linear algebra: vector spaces, bases and dimension; matrices and their properties, matrix operations, rank and determinant; linear systems of equations, existence of solutions, cases of one solution and infinitely many solutions, Gaussian elimination, inverse of a matrix and Cramer's rule; eigenvalues and eigenvectors.

Calculus

One-variable functions: basic definitions, graphs and elementary functions (linear, quadratic, polynomial, rational, irrational, power, exponential, logarithmic, absolute value). Odd and even functions. Composite functions. Inverse functions.

Limits and continuity.

Differentiation of one-variable functions: tangents and derivatives, rules of differentiation, chain rule, higher-order derivatives.

Derivatives in use: implicit differentiation and economic examples, differentiation of the inverse function, linear and quadratic approximations, Taylor's formula, elasticities; continuity and differentiability, intermediate-value theorem, De L’Hôpital’s Rule.

Single-variable optimization: local and global extrema, stationary points and first-order condition, simple tests for extreme points, extreme points for concave and convex functions, second-order derivative and convexity, inflection points, study of the graph of a function, asymptotes.

Integration: the Riemann integral and its geometrical interpretation; primitives and indefinite integrals, fundamental theorems of integral calculus. Rules and methods of integration: immediate integrals, integration of rational functions, integration by parts, integration by substitution. Improper integrals.

Multi-variable calculus: partial derivatives with two variables, geometric interpretation;differentials and linear approximations.

Multi-variable optimization; maxima, minima and saddle points; tests based on second derivatives.

Testi/Bibliografia

K. Sydsaeter, P. Hammond, and A. Strom

Essential Mathematics for Economic Analysis

4th Edition, Pearson 2012

Metodi didattici

Lectures and excercises at the blackboard.

Modalità di verifica e valutazione dell'apprendimento

Partial written exams, according to the academic terms. As an alternative, cumulative written exam.

Strumenti a supporto della didattica

Professor's lecture notes

Orario di ricevimento

Consulta il sito web di Gian Luca Tassinari