Learning outcomes of the course unit
Knowledge and ability to understand. At the end of the course the student should have acquired knowledge and skills regarding the basic algorithms of numerical calculation. In fact one of the main purposes of the course is to provide the mathematical and applicative basics of algorithms that are the basis of Numeric Calculation, Both theoretical and applied properties, show examples and counterexamples illustrating the advantages and weaknesses. This presentation should also lead the student to develop a critical sense on the most appropriate methodology to solve numerically different elementary problems numerically. During the course, individual and team workouts will be proposed, such exercises will address some elementary applications in a simple and fairly universal software environment such as MATLAB. In addition, the student should be able to present clearly and accurately the contents of the program, especially in an application context. Such skills will also be developed in a direct confrontation with the lecturer in frontal and laboratory lessons. Starting from the basic and fundamental knowledge provided by the course and the laboratory, the student will be able to consult the autonomous texts specialized in order to deal with the workplace as well.
Basics: Calculus and Linear Algebra.
Course contents summary
Error Analysis - Approximation of data and functions - Numerical integration: Newton-Cotes formulas - Systems of linear equations: direct methods, factorization, iterative methods - Non-linear equations - Introduction to MATLAB
Error analysis - Rounding errors - Conditioning of a problem and stability of an algorithm - 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 - Numerical integration: interpolatory quadrature formulas: Newton-Cotes integration, Formule composed, Error estimates, Applications of quadrature formulas - Numerical linear algebra: direct methods, the method of Gaussian elimination, Gauss decomposition and LU factorization, Matrix inverse - Iterative methods: Jacobi method, Gauss-Seidel method - Non-linear equation: bisection method, the tangents (Newton-Raphson) method, test of convergence, iterative methods in general. Matlab.
G.Naldi, L: Pareschi, G.Russo, Introduzione al Calcolo Scientifico, Mc Graw-Hill.
G.Monegato Fondamenti di Calcolo Numerico, CLUT.
L. Scuderi, Laboratorio di Calcolo Numerico, CLUT.
Lectures and immediate classroom exercises on the topics of the last lessons you have taken. MATLAB exercises in numerical laboratory. Correction of individually assigned assignments and groups.
Assessment methods and criteria
Verification of learning takes place in a traditional way through the evaluation of an oral test in which students will be offered simple simple numerical exercises and / or simple MATLAB programming.