69176 - Numerical Methods for Computation

Learning outcomes

The general ideas and concepts of scientific computation and error analysis are introduced. The lessons are mostly concerned with the treatment of traditional mathematical problems and the aspects which are of importance for the design of algorithms are examined in Matlab/Octave environment

Course contents

Ecco una traduzione naturale e adatta a un syllabus o programma di corso:

• Finite-precision arithmetic

• Nonlinear equations

• Functions of several variables: differentiability

• Minimization of functions of several variables: the gradient method

• Numerical linear algebra: norms, linear systems, conditioning, eigenvalues, singular values, linear regression, and least squares

• Interpolation and approximation

• First-order ordinary differential equations: the Euler method

• Python: NumPy, SciPy, Matplotlib, and scikit-learn libraries

The topics will be covered both from a theoretical perspective and through Python implementations of the corresponding algorithms.

Four homework assignments will be given.

Readings/Bibliography

notes of the teachers

Teaching methods

lectures and guided laboratories

Assessment methods

Here is a natural and formal English translation suitable for a course syllabus:

The examination consists of two parts, both taken on the same day: a multiple-choice quiz (three options per question) and an oral examination.

The multiple-choice quiz consists of 20 questions covering both theoretical topics and simple exercises from the entire course syllabus. Each correct answer is worth one point, while incorrect or unanswered questions receive zero points. The maximum score is 20 points. A minimum score of 14 points is required to be admitted to the oral examination. 

The quiz is taken on the University of Bologna's Virtuale platform using the student's own laptop. Students are allowed to use a calculator only.

The oral examination is based on the homework assignments. Students are required to bring their uncommented source code and a report containing only the obtained results (figures and tables).

The oral examination consists of a discussion of the homework assignments. Questions may concern the code, the obtained results, and the theoretical concepts related to the homework. The maximum score is 12 points, and the minimum passing score is 4 points. Assessment is based on the efficiency of the code, the student's understanding of the code, the quality of the obtained results, and the ability to explain the relevant theoretical concepts.

The final grade is the sum of the scores obtained in the two parts of the examination. If the total score exceeds 30, the student is awarded 30 cum laude.

If either part of the examination is not passed, the entire examination must be retaken.

 

Here is a clear and formal English version suitable for an exam policy:

With regard to the oral exam, limited and non-substantial use of AI is permitted for support activities (e.g., code checking and documentation). Substantial use of AI to complete any part of the project is not permitted. During the oral examination, students must demonstrate a thorough understanding of their code, be able to explain how it works, and justify the implementation choices they made.

Office hours

See the website of Elena Loli Piccolomini

See the website of Carolina Vittoria Beccari