73183 - Numerical Methods M

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 and to apply the knowledge of these methods to solve practical problems with the aid of a scientific computation software.

Course contents

The student has the knowledge of mathematical analysis and geometry taught in courses of Mathematical Analysis and Geometry of the Environmental Engineering Bachelor course. All lectures are given in Italian. It is therefore necessary to understand the Italian language to successfully attend the course and to be able to use the educational material provided.

Course contents (divided by module):

Module 1 (24 hours):

• Presentation of the Matlab environment and the various aspects of programming within the main themes proposed
• Machine Numbers: rounding and truncation errors
• Problem conditioning and algorithm stability
• Nonlinear Equations and Systems of Equations

Module 2 (24 hours):

• Linear Systems of Equations
• Least Squares Approximation
• Ordinary Differential Equations: Initial Value Problems
  

 

Readings/Bibliography

• U. M. Ascher, C. Greif, A First Course on Numerical Methods, SIAM, 2011.

• Steven C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3/e Mc Graw Hill, 2017.

Teaching methods

• Lectures and guided laboratory exercises (Matlab).

• IoL learning tools and Matlab Academy modules (https://matlabacademy.mathworks.com).

Assessment methods

Final laboratory exam: 30% theory, 70% exercises to be solved by using Matlab. 

The total number of points of the final test is 32/30, which corresponds to the 30 cum laude grade.

The exam execution modalities (in presence, remotely,...) will be esatblished according to the conditions/prescriptions existing at the time of the exam itself.

Teaching tools

The teaching materials will be available on the e-learning platform.

Office hours

See the website of Alessandro Lanza

See the website of Fabiana Zama