MODELLING FOR THE ENVIRONEMENT AND SAFETY
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Delivery method
- Teaching methods
Linear Algebra and Calculus.
Written and oral exam
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
Classroom teaching; practical exercises