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, eigenvectors and eigenvalues.

MATRIXES: Classification, properties and operations. Characteristics of a matrix; Condensation; Inverse of a square matrix; Resolution of matrix equations.

DETERMINANTS: Definitions and properties; Calculation of determinants by Sarrus's rule, Laplace's theorem and triangulation method; Obtain the inverse by the adjunct.

SYSTEMS OF EQUATIONS: Classification and resolution. Gaussian Method and Cramer's Rule.

VECTOR SPACES: Vectors and operations. Definition and properties; Linear combination; Linear dependence and independence; Vector subspace; Set of generators; Base and dimension of a vector space; Change of base.

EIGENVALUES AND EIGENVECTORS: Definition, properties and their determination. Diagonalization. Quadratic form. Applications.

This UC will use some active methodologies that promote greater student involvement in pedagogical activities, such as Problem Based Learning in a collaborative environment. In terms of digital technologies, Moodle 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.