At the end of the course, students should be capable of applying the basic numerical methods for scientific computing, as well as skilled in programming in Matlab. Students must have a deep knowledge about the following concepts: - floating point number representation and roundoff errors, algorithm, programming language - numerical methods and numerical solution - convergence of itrative methods - convergence rate, - approximation error - discretization of 1D interval. Moreover, they must be capable of programming in Matlab the metodhs.
Course Prerequisites
Students are required to be familiar with basic concepts of Linear Algebra, Analytic Geometry, and Mathematical Analysis. In particular, to follow the course profitably, students must possess the following skills and competences: - to be familiar with vector and matrix calculus; - to know how to handle scalar and vector fields, gradients, Jacobian matrix and Hessian matrix; - knowledge of the theory of ordinary differential equations. All the topics listed above are strong prerequisites to follow the course and fully learn the contents.
Teaching Methods
1. Frontal lectures to illustrate the definition and properties of the numerical methods 2. Matlab sessions for the implementation of the numerical methods
Assessment Methods
The final exam is written and possibly oral. The written exam is made by two parts: the first one at the end of the first semester, and the second one at the end of the second semester. In alternative, the written exam can be taken only once starting from the end of the second semester. If the written exam is passed (evaluation greater or equal than 18), an oral examination is compulsory if the evaluation of the written part is lower than 24, otherwise the oral exam is optional.
Texts
Quarteroni, Alfio, Saleri, F., Gervasio, Paola, "Calcolo Scientifico, Esercizi e problemi risolti con MATLAB e Octave", Springer, 2016
Contents
Introduction to scientific computing - Function zero finding - Polynomial interpolation and least square methods - Numerical quadrature - Numerical linear algebra, eigenproblems, direct and iterative methods for linear systems - Numerical methods for ordinary differential equations
