M.G. Gasparo, R. Morandi: "Elementi di calcolo Numerico: metodi ed algoritmi", Mc-Graw Hill, 2008.
G. Naldi, L. Pareschi, G. Russo, "Introduzione al calcolo Scientifico, metodi e applicazioni con Matlab", McGraw-Hill, 2001.
A. Quarteroni, R. Sacco, F.Saleri, "Matematica Numerica", Springer 2000.
Learning Objectives
Knowledge of the most used numerical methods for solving linear and nonlinear equations, interpolation and regression problems.
Ability to develop an algorithm for the methods studied
Prerequisites
Fundamentals of linear algebra and calculus
Teaching Methods
Lectures (39 hours) and Matlab laboratory (15 hours)
Further information
The schedule of the exams is available at the webpage of the School of Engineering
E-Learning with Moodle is available
Type of Assessment
Written exam consisting in the solution of problems discussed in the course (floating-point arithmetics, linear systems, nonlinear equations, interpolation and least-squares approximation, quadrature rule) and the development of a Matlab function. The cut score for passing is 18/30. Students that pass the writte exam will take an oral exam on the topics of the course, with particular attention to the definition and properties of the numerical methods studied.
Students can take the examination after passing the exam on Geometry and Linear Algebra
Course program
Algorithms. Floating point arithmetics. Finite precision. Norms of matrices and vectors.
Conditioning of a problem.
Stability of an algorithm. Direct methods for linear systems: Gauss method and pivoting strategies. Jacobi and Gauss-Siedel iterative methods for linear systems.
Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; corresponding algorithms.
MATLAB: Handling matrices, operations between matrices. Function and script files.
If, while and for commands.
2D e 3D plots. Built-in functions for linear systems, nonlinear equations, basic fitting.