37292 - MATHEMATICS

Scheda insegnamento

Anno Accademico 2021/2022

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: differentiation of the inverse function, linear and quadratic approximations, Taylor's formula; 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 by parts.

Apprications to Calculus of Probabilities

Multi-variable calculus: partial derivatives with two variables, geometric interpretation. Multi-variable optimization; maxima, minima and saddle points.

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.

Online Presentations. Software Geogebra

Modalità di verifica e valutazione dell'apprendimento

Written exam (in presence): students have to solve different exercises on the course topics. To each exercise a given maximum number of point is associated, and to get it the student has to solve correctly the exercise and all the steps must be justified. The theoretical maximum number of points in case of a perfect exam is 32. The test assessment grid will be as follows:

· <18 insufficient

· 18-23 sufficient

· 24-27 average/good

· 28-30 very good

· 30 cum laude excellent/outstanding

If your total is <=30 score, your score corresponds to your mark. If your score is >30, then you get 30 cum laude.

Oral exam (online): The theoretical maximum number of points in case of a perfect exam is 25/30.

The exam of the first session can be taken in 2 steps: a first midterm exam (after 1/2 of the course, during the mid-term session of November) with a duration 1 hour and 20 min., a second partial exam with a duration of 1 hour and 20 min. on January. During the session of June/July and September the exam will be about the full program, with a test duration of 2 hours and 40 min.

Strumenti a supporto della didattica

Professor's lecture notes. Excercises at the blackboard.

Online Presentations. Software Geogebra

Orario di ricevimento

Consulta il sito web di Donatella Giuliani