Enrollment year
2016/2017
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
INDUSTRIAL ENGINEERING
Curriculum
PERCORSO COMUNE
Period
2nd semester (01/03/2017 - 09/06/2017)
Lesson hours
83 lesson hours
Activity type
WRITTEN AND ORAL TEST
Prerequisites
Analisi Matematica I, Geometria e Algebra.
Learning outcomes
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.
Course contents
Mathematical Analysis
Series; absolute and simple convergence; series with positive terms; special series. Convergence results. Power series; derivation and integration. Taylor expansion.
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.
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.
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
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.
Inferential statistics; confidence intervals for the mean value and the variance. Linear regression.
Teaching methods
Lectures (hours/year in lecture theatre): 35
Practical class (hours/year in lecture theatre): 65
Practicals / Workshops (hours/year in lecture theatre): 0
Reccomended or required readings
M. Bramanti, C. D. Pagani, S. Salsa. Analisi Matematica 2. Zanichelli, 2009.
P. Baldi. Introduzione alla probabilità con elementi di statistica. McGraw-Hill.
Assessment methods
The exam consists in two written tests (one for the analysis part and one for the statistics part) and an oral examination. The rules are aivalable at the web page of the course
Further information
The exam consists in two written tests (one for the analysis part and one for the statistics part) and an oral examination. The rules are aivalable at the web page of the course
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