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: stability, accuracy, algorithmic complexity, and show examples and counterexamples which illustrate the advantages and weaknesses. It also aims to test the algorithms presented in a simple and fairly universal software such as MATLAB.
Basics: Calculus and Linear Algebra
Course contents summary
Approximation of data and functions
- Numerical integration: Newton-Cotes formulas, formulas composed, formulas for integrals in multiple dimensions (Hint).
-Linear systems: direct methods, method eleiminazione Gauss factorization.
-Non linear equations.
-Introduction to Matlab.
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, according to Newton-Cotes Integration, Error estimates, Formule composed, Applications of quadrature formulas.
Numerical linear algebra: direct methods, the method of Gaussian elimination, Gauss decomposition and LU factorization. Equations and nonlinear systems: real roots of nonlinear equations, bisection method, secant methods, Newton-Raphson method.
G. Monegato, Fondamenti di Calcolo Numerico, CLUT.
Lectures and exercises in the classroom. MATLAB numerical exercises in the laboratory. Correction of exercises assigned individually
Assessment methods and criteria
Exercises followed by an oral examination.