Numerical Analysis

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/08 Numerical Analysis.

Examination method

Written or laboratory exam and oral exam.

Learning
objectives

This course aims to deepen and broaden the knowledge of Numerical Analysis provided in the course Programming and Computing Laboratory, addressing advanced topics and methods, with attention to issues of convergence, consistency, numerical stability and computational complexity. It also aims to provide methodologies for the design, development, analysis and use of mathematical software. The related laboratory work will involve implementing algorithms in a high-level programming language and using Problem Solving Environments (PSE).

Syllabus

Direct and iterative methods for solving linear systems and least squares problems; minimisation of quadratic functions, eigenvectors and eigenvalues, quadrature. Minimisation of C1 functions and solution of systems of nonlinear equations; approximation theory. Introduction to the solution of ordinary differential equations, partial differential equations and the numerical solution of integral equations. Use of MATLAB (or an equivalent PSE) and of the C/C++ programming language.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

know and understand the methodological foundations of numerical mathematics, showing that they can rigorously formulate and solve scientific computing problems relating to the topics of the course;
are able to apply the knowledge acquired by designing and implementing algorithms based on the numerical methods covered, critically analysing the results obtained and taking into account the influence of the finite-precision computing environment on those results;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Ability to develop algorithms and programs of varying difficulty independently using numerical techniques; clarity, correctness and completeness in the oral presentation of the course topics.

Numerical Analysis