# MODELLING FOR THE ENVIRONEMENT AND SAFETY

Degree course:
Corso di First cycle degree in ENGINEERING FOR WORK AND ENVIRONMENT SAFETY
Academic year when starting the degree:
2018/2019
Year:
2
Academic year in which the course will be held:
2019/2020
Course type:
Basic compulsory subjects
Language:
Italian
Credits:
6
Period:
First Semester
Standard lectures hours:
48
Detail of lecture’s hours:
Lesson (48 hours)
Requirements:

Linear Algebra and Calculus.

Final Examination:
Orale

Written and oral exam

Assessment:
Voto Finale

Basic knowledge for understanding a constructive mathematical approach and for implementing on a
computer algorithms of numerical type, accompanied by the ability of reading and interpreting the results.
A key goal is to acquire the tools for evaluating stability and complexity of the considered methods, especially in connection with models coming from real world applications.

Revisiting Linear Algebra on the complex field from a constructive viepoint

Basic matrix theory. Unitary, Hermitian, positive definite matrices.
Elementary matrices (Gauss, Householder)

Numerical solution of linear systems: coefficient matrices in special form (unitary, triangular etc)
Numerical solution of linear systems: Gaussian elimination, pivoting, QR factorization
Iterative solvers: Jacobi, Gauss-Seidel
Evaluation of a polynomial at a point. Interpolation. Least squares

Revisiting Linear Algebra on the complex field from a constructive viepoint
Basic matrix theory. Unitary, Hermitian, positive definite matrices.
Elementary matrices (Gauss, Householder)
Numerical solution of linear systems: coefficient matrices in special form (unitary, triangular etc)
Numerical solution of linear systems: Gaussian elimination, pivoting, QR factorization
Iterative solvers: Jacobi, Gauss-Seidel
Evaluation of a polynomial at a point. Interpolation. Least squares

“Introduction to Numerical Analysis”, J. Stoer, R. Bulirsh, Springer
“Matematica numerica”, A. Quarteroni, R. Sacco, F. Saleri, P. Gervasio, Springer
“Metodi Numerici per l’Algebra Lineare”, D. Bini, M. Capovani, O. Menchi, Zanichelli
“Metodi Numerici”, R. Bevilacqua, D. Bini, M. Capovani, O. Menchi, Zanichelli
“Scientific Computing with Matlab and Octave”, A. Quarteroni, F. Saleri, Springer

Convenzionale

Classroom teaching; practical exercises