Enrollment year
2015/2016
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
INDUSTRIAL ENGINEERING
Curriculum
PERCORSO COMUNE
Period
2nd semester (29/02/2016 - 10/06/2016)
Lesson hours
82 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 of two parts: written and oral. Admission to the oral exam only if the result of written exam is not less than 16/30. Both exams must be completed in the same session. The written test takes places on the day of the beginning of the exam session; the oral exam will start few days later.
Further information
The exam consists of two parts: written and oral. Admission to the oral exam only if the result of written exam is not less than 16/30. Both exams must be completed in the same session. The written test takes places on the day of the beginning of the exam session; the oral exam will start few days later.
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