Linear Algebra and Geometry I

Code: MAT00900L

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: Presencial

Presentation

This curricular unit addresses the basic concepts and tools of Linear Algebra and Analytical Geometry and their applications.

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

The main outcomes of the course are acquire concepts and basic tools of Linear Algebra and Analytic Geometry and their applications. Students are expected to be able to use the various contents in order to use them skillfully and with critical sense in other areas of Mathematics, Engineering, Economics and Management. It is also intended to introduce students to mathematical argumentation in order to develop correct reasoning, working different methods of proof making, not diminishing the rigor in language.

Systems of linear equations.
Matrices.
Determinants.
Vector spaces.
Linear applications.
Eigenvalues and eigenvectors.
Geometry of plane and space.
Quadratic forms.

Teaching Methods

This is a course with 2h of theoretical lessons and 2h of practical lessons per week. In there will be a structured exposition of the subjects using examples, when possible, with emphasis on relevant applications. Given the pedagogical model adopted, the exposure of such knowledge is complemented with the resolution of exercises that are previously provided. For a proper understanding of the syllabus, students should develop regular work outside the classroom, particularly in the study of concepts and solving exercises. In the recommended bibliography there are several exercises, some of them already solved, that can contribute significantly to the success of the learning. Complementary, there exists weakly periods of individual attendance.

Assessment

Evaluation can be done along the semester, by doing two tests and five minitests, or by final exam. The final grade of the evaluation along the semester is the weighted mean of the two tests (90%) and the five minitests (10%). There is a minimum grade of 7.5 in each test. If this weighted mean is lower than the simple mean of the two tests, the latter will prevail. A student who has less tham 7.5, but at least 5 in the first test may do extra questions in the second to recover the grade. Students who have 18 or more will do an oral exam, and the final grade will be the minunum between 17 and the simple mean between the previous grade and the grade of the oral exam.