73750 - Numerical Methods T

Learning outcomes

Natural phenomena of physical interest, as well as artificial industrial processes, are modelled by complex systems that hardly ever admit an analytical solution from the mathematical point of view. Computational methods allow us to approach the problem and to find a solution efficiently, albeit in an approximate form. In order to understand the potentialities and limitations of these computational methods, it is of fundamental importance to analyze their accuracy and understand aspects such as stability, efficiency and robustness of a numerical scheme. The course aims to introduce fundamental concepts of numerical analysis, emphasizing applicability and limitations of the basic numerical algorithms used to provide solutions to common problems in science and engineering. On successful completion of the course, students will be able to understand common numerical methods, how they are used to obtain approximate solutions to otherwise intractable mathematical problems, how to apply the knowledge of these methods to solve practical problems with the aid of a scientific computation software and, finally, to critically evaluate the results obtained.

Course contents

• Introduction to algorithms and data structures.
• Brief mentions on machine numbers; conditioning of a problem and stability of an algorithm.
• Algorithms for solving non-linear equations.
• Approximation of experimental data: least squares principle, linear regression. Brief mentions on non-linear regression. Matlab is the working tool for theory verification and examples. It will be introduced and explored throughout the course.

Readings/Bibliography

Books suggested (for in-depth study of the topics of the course):

- A. Quarteroni, R. Sacco, F. Saleri, "Matematica Numerica", Springer (2008);

- A. Quarteroni, F. Saleri, "Calcolo Scientifico. Esercizi e problemi risolti con Matlab e Octave", Springer (2008);

- G. Naldi, L. Pareschi, "Matlab. Concetti e progetti", Apogeo (2007), or Morzenti, A. Campi, E. Di Nitto, P. Spoletini, D. Loiacono, "Introduzione alla programmazione in Matlab", Esculapio (2011).

Teaching methods

Theoretical lectures and guided laboratory exercises (Matlab).

Given the type of activity and teaching methods adopted, the attendance of this course requires the prior participation of all students in the training modules 1 and 2 on safety in the study places ( https://elearning-sicurezza.unibo. it/ ) in e-learning mode.

Assessment methods

Attendance to the lessons is not mandatory nor will it be considered for the final evaluation, but it is highly recommended to maximize the teaching impact and to easy the students' learning.

The final exam (on the arguments of both modules) consists of a practical test containing exercises that require the analysis and preparation of Matlab codes. The test is aimed at ascertaining the skills acquired in solving mathematical problems using numerical methods implemented in Matlab.

Personal notes, codes and texts are not allowed in the test.

The test will assign a score from 0/30 to 30/30. The test is passed with a minimum score of 18/30.

Teaching tools

Slides provided by the teacher. The teaching material will be available on the University of Bologna e-learning platform (https://virtuale.unibo.it).

Office hours

See the website of Fabiana Zama