2018/2019

2018/2019

DM270

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

INDUSTRIAL ENGINEERING

PERCORSO COMUNE

1°

2nd semester (06/03/2019 - 14/06/2019)

9

83 lesson hours

Italian

WRITTEN AND ORAL TEST

FORNARO SIMONA (titolare) - 6 ECTS
PRIOLA Enrico - 3 ECTS

Student are expected to master the notions presented in the courses Analisi Matematica I, and Geometria e Algebra.

This is a second course in calculus and a first course in mathematical probability with an introduction to statistical inference. It includes series, vector analysis, multiple integrals, line and surface integrals, the integral theorems of vector calculus; moreover, the calculus of probability, combinatorial analysis, independence, conditional probability, Bayes' theorem, random variables, expectation, variance, distribution functions, law of large numbers and central limit theorem; interval estimation.

Mathematical Analysis
1. Series; absolute and simple convergence; series with positive terms; special series. Convergence results. Power series; derivation and integration. Taylor expansion.
2. Calculus for functions of several variables. Limits, continuity, partial derivatives, gradient, differentiability, Hessian; stationary points and their classification. Taylor's formula. Calculus for vector functions; Jacobian.
3. Multiple integrals. Two dimensional integrals; change of coordinates, polar coordinates, techniques of integration. Three dimensional integrals: spherical or cylindrical coordinates; evaluating the integral by the slice method or the line method.
4. Line and surface integrals. Parametric equations of a line; tangent line; arc lenght. Parametric equations of a surface; tangent plane; surface area; surface of revolution. Line integrals of scalar fields and of vector fields. Conservative vector fields. The differential operators curl and div. Surface integrals. Green's theorem; Stokes' theorem; divergence theorem.

Statistics
1. Definition of probability. Conditional probability; Bayes' theorem. Independence. Mathematical expectation, variance. Random variables; discrete and continuous. Chebyshev inequality. Law of large numbers. Central limit theorem. Student's t-distribution and chi-square distribution.
2. Inferential statistics; confidence intervals for the mean value and the variance. Linear regression.

Lectures (hours/year in lecture theatre): 45
Practical class (hours/year in lecture theatre): 38
Practicals / Workshops (hours/year in lecture theatre): 0

M. Bramanti, C. D. Pagani, S. Salsa. Analisi Matematica 2. Zanichelli, 2009.
M. Bramanti. Calcolo delle Probabilità e Statistica. Teoria ed Esercizi. Esculapio.

The exam consists in a written test, made up of two parts (one of analysis, and one of statistics) and an oral examination, which is not compulsory, for all the students who passed the written test with a positive mark.

The exam consists in a written test, made up of two parts (one of analysis, and one of statistics) and an oral examination, which is not compulsory, for all the students who passed the written test with a positive mark.