Learning outcomes of the course unit
One of the main aims of the course is to provide the mathematical foundation underlying the different methods or algorithms, recall the main theoretical properties and show examples and counterexamples whic illustrate the advantages. It also aims to test the algorithms presented in a simple and fairly universal software such as Matlab.
Basic: calculus and Linear Algebra.
Course contents summary
Approximation of data and functions (14 hours)- Numerical integration: Newton-Cotes formulas (8 hours) - Systems of linear equations: direct methods, factorization (14 hours) - Non-linear equations (6 hours) - Introduction to Matlab (4 hours)
Accuracy of data and functions: polynomial interpolation, Lagrange interpolation formula, Hermite interpolation formula, the formula of Newton divided differences, interpolation of piecewise polynomial functions, spline functions, interpolation of functions of several variables (hint).
Numerical integration: interpolatory quadrature formulas, according to Newton-Cotes Integration, Error estimates, Formule composed.
Numerical linear algebra: direct methods, the method of Gaussian elimination, Gauss decomposition and LU factorization, matrix inverse. Non linear equations: bisection method.
G.Naldi, L. Pareschi, G. Russo, Introduzione al Calcolo Scientifico, McGraw-Hill.
G. Monegato, Fondamenti di Calcolo Numerico, CLUT.
Lessons and exercises in the classroom. Delivery of exercises assigned individually and/or to groups to be developed and resolved.
Assessment methods and criteria
Written exam with exercises similar to those assigned in the exercises. Oral exam.
You are exempted from the written test if the proposed exercises are delivered during the course.