Learning outcomes of the course unit
Numerical analysis, in essence, is a branch of mathematics which deals with the numerical and therefore constructive solution of problems, formulated and studied in other branches of mathematics. One of aims of this course is to present background material of several numerical methods in branches of mathematics with which numerical analysis has made its principal contacts.
First principles of Analysis and Geometry
Course contents summary
Interpolation and Approximation. Polynomial interpolation. Hermite interpolation. Splines. Least-square approximations. Trigonometric interpolation.
Solution of linear system of equations. Gauss elimination. Operations counts. Pivoting and Scaling in Gauss elimination. LU decompositions.
Numerical integration. Newton-Cotes Formulas. Composite formulas. Error estimate.
Solution non-linear equations. Bisection. Newton method in one variable. Secant method. Construction. Practical considerations.
Introduction to Matlab
G.Naldi, L.Pareschi, G. Russo, Introduzione al Calcolo Scientifico (metodi e applicazioni con Matlab), McGraw-Hill.
G.Monegato, Fondamenti di Calcolo Numerico, CLUT, Torino.
William J. Palm III, Introduction to MATLAB 7 for engineerings, McGraw-Hill.
Oral lesson and laboratory
Oral exam and practical test