Class Linear Algebra

The Linear Algebra course provides the essential mathematical foundations for Engineering education, enabling the modelling and solution of scientific and technological problems. Its scope covers real and complex numbers, matrices, systems of linear equations, determinants, vector spaces, linear transformations, and eigenvalues and eigenvectors. The course develops students' ability to apply algebraic methods to analyse and solve engineering problems, providing a foundation for areas such as scientific computing, control systems, signal processing, artificial intelligence, and data science. Within the study programme, this course plays a fundamental role by supporting subsequent engineering courses and fostering logical reasoning, abstract thinking, and the application of mathematical methods to engineering problem-solving.

Not applicable

1. Matrices 2. Systems of linear equations 3. Determinants 4. Linear spaces 5. Linear transformations 6. Eigenvalues and eigenvectors

A series of exercises will be proposed to consolidate students' knowledge and develop their problem-solving skills. In each class, students are encouraged to work on questions related to the topics covered and to present the results of their individual work in the following session. Throughout the course, particular emphasis is placed on the fundamental idea that solving exercises is not an end in itself, but rather a means of achieving a deeper understanding of the underlying mathematical concepts. Mastery of these concepts enables students to apply the acquired techniques to the solution of more advanced engineering and scientific problems. To further support learning and promote student engagement, short videos on selected course topics, historical notes, mathematical curiosities, recreational problems, and real-world applications will be made available throughout the course.

Cabral, I., Perdigão, C., & Saiago, C. Álgebra Linear: Teoria, Exercícios Resolvidos e Exercícios Propostos com Soluções. 7.ª ed., Forte da Casa: Escolar Editora, 2024.