2013/2014

2014/2015

DM270

MAT/08 (NUMERICAL ANALYSIS)

DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE

CIVIL AND ENVIRONMENTAL ENGINEERING

PERCORSO COMUNE

2°

1st semester (29/09/2014 - 16/01/2015)

6

56 lesson hours

ITALIAN

WRITTEN AND ORAL TEST

BOFFI DANIELE - 3 ECTS
GUGLIELMANN RAFFAELLA - 3 ECTS

Differential and integral calculus for real value functions, complex numbers, vector and matrix calculus. Practical computer skills.

The course provides an introduction to the basic tools of Numerical Analysis and Programming. In particular, the course aims at showing the most commonly used algorithms for the solution of practical problems. The algorithms are presented with the help of Matlab software.

The course is split into two parts: Numerical computing and Computing. The first part is taught in the first semester, the second part in the second one. Both parts contains theoretical and practical lectures.

Numerical analysis: here is the list of subjects.

Nonlinear equations: bisection method, Newton method. Convergence and convergence order. Stopping criteria.
Approximation of functions and data: Lagrange interpolation, piecewise polynomial interpolation; least square method and data fitting: linear regression.
Numerical integration and differentiation: Approximation of the derivative. Quadrature rules: midpoint, trapezoidal, and Simpson rules. Gauss formulae.
Direct solvers for linear system: condition number and eigenvalue problems. Gaussian elimination and LU factorization; implementation and complexity of LU factorization; symmetric and positive definitive matrices: Cholesky factorization.
Iterative solvers for linear systems: Jacobi, Gauss-Seidel, and relaxation; implementation and convergence; stopping criteria.
Numerical solution of ordinary differential equations: one-step methods: forward and backward Euler, Crank-Nicolson, Heun; stability and A-stability, consistency, convergence and convergence order; computational aspects.

The Matlab programming language: variables and expressions; control structures; functions and recursion.

A. Quarteroni, F. Saleri , P. Gervasio. Calcolo scientifico: Esercizi e problemi risolti con MATLAB e Octave (V ed.). Springer, 2012.

Written midterm exam at the end of the first semester (numerical analysis); written midterm exam at the end of the second semester (programming) for students who passed the first midterm exam. Written exams on the entire program for student who fail the midterms.
Oral exam for students who do not reach a prescribed threshold.
More details are available from the web page: http://www-dimat.unipv.it/gugliel/teaching.htm