Class Algebra

The present curricular unit belongs to the curricular plan of this 1st cycle degree. The main goal of this curricular unit is to provide students with fundamental knowledge in the context of algebra and mathematical and logical reasoning, that are essential in learning the contents of other subsequent curricular units. It is intended that, through various theoretical and practical strategies, students can apply and solidify the knowledge gained throughout the semester on vector spaces, matrices, determinants, systems of linear equations, complex numbers, eigenvectors and eigenvalues and linear transformations.

Not applicable

1. Review of sets and complex numbers. MATLAB software environment. 2. Matrices: classification, properties, and operations. Matrix rank. Inverse of a matrix. Matrix equations. 3. Determinants: definitions and properties; calculation using Sarrus’ Rule, Laplace’s Theorem, and the triangularization method; finding the inverse using the adjugate. 4. Systems of equations: classification and methods of solution. 5. Vector spaces: vectors and operations; definition and properties; linear combination; linear dependence and independence; vector subspace; generating set; basis and dimension of a vector space; change of basis. 6. Eigenvalues and eigenvectors: definition, properties, and determination. Diagonalization. Quadratic form. Applications. 7. Linear transformations: kernel and image. Matrix representation of a linear transformation.

This UC will use some active methodologies that promote greater student involvement in pedagogical activities, such as Flipped Classroom  and learning in a collaborative environment. In terms of digital technologies, Moodle and MATLAB will be used.

- Giraldes, E., Fernandes, V., Smith, M. (2003), Curso de Álgebra Linear e Geometria Analítica, McGraw Hill, Portugal. - Kreyszig, E. (2011), Advanced Engineering Mathematics (tenth edition), McGraw Hill, United States of America. - Diversos textos de apoio a fornecer ao longo das sessões.