Numerical Analysis Methods

Numerical Analysis Methods - Part A
teacher: Professor Donatella Occorsio
Language of the lessons
Italian
Short Contents
Approximation of periodic functions. Approximation by poynomials on unboinded intervals.
Quadrature rules of Gaussian and Product types ovre bounded and unbounded intervals.
Bibliography
G. Monegato, Fondamenti di Calcolo Numerico, Edizioni C.L.U.T. Torino, 1998
George P. Tolstov Fourier Series, Dover edition 1962
G. Mastroianni, G.V. Milovanovic: Interpolation processes. Basic theory and applications,
Springer Verlag, Berlin 2008
Appunti in formato pdf e presentazioni redatte dal docente
Notes and handouts of the teacher.
Educational objectives
In the Part A the student is introduced to the basic notions of the Approximation Theory. These will
be suitable selected for studying numerical methods for the solution of Integral equations, developed
in the Part B of the same course. Moreover, the case of periodic functions will be extensively
treated. An adequate knowledge of Matlab programming will be achieved, as basic tool in the
actual understanding of the main topics,
Prerequisites
The knowledge of the arguments from Calculus and Linear Algebra, Numerical Analysis,
from Computer Science and basic Programming in Matlab .
Teaching methods
Lectures and laboratory programming work .
Assessment methods
Oral and practical exam
Detailed contents
Approximation of periodic functions by Fourier sums and Lagrange polynomials
Approximation by polynomials in weighted uniform spaces.
Gaussian rules over unbounded intervals
Product Integration rules for weakly singular integrals
skills