2024
Linear Algebra and Geometry I
Name: 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
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.
Contents
Systems of linear equations.
Matrices.
Determinants.
Vector spaces.
Linear applications.
Eigenvalues and eigenvectors. Jordan canonical form.
Geometry of plane and space.
Quadratic forms.
Matrices.
Determinants.
Vector spaces.
Linear applications.
Eigenvalues and eigenvectors. Jordan canonical form.
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.
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 methods:Two tests (the final grade is your average, if it is equal to or greater than 10/20 with a minimum grade of 7.5/20 in each test) or final exam with 100% weight in the final classification.
Recommended Reading
Bibliography for A.L.G.A.
1 - Dias Agudo, F.R., "Introdução à Álgebra Linear e Geometria Analítica", Livraria Escolar Editora
2 - Greub, W., "Linear Algebra", Springer
3 - Lipschutz, S., "Álgebra Linear", McGraw-Hill
4 - Magalhães, L.T. "Álgebra linear como introdução à matemática aplicada", Texto editora
5 - Monteiro, A.J.A., "Álgebra Linear e Geometria Analítica", edição da Associação de Estudantes da FCUL
6 - Silva Ribeiro, C., "Algebra linear: exercícios e aplicações", McGraw-Hill
Note: we only know truly 1,2 and 5. There are plenty of books of Álgebra Linear in section M15 of the library.
1 - Dias Agudo, F.R., "Introdução à Álgebra Linear e Geometria Analítica", Livraria Escolar Editora
2 - Greub, W., "Linear Algebra", Springer
3 - Lipschutz, S., "Álgebra Linear", McGraw-Hill
4 - Magalhães, L.T. "Álgebra linear como introdução à matemática aplicada", Texto editora
5 - Monteiro, A.J.A., "Álgebra Linear e Geometria Analítica", edição da Associação de Estudantes da FCUL
6 - Silva Ribeiro, C., "Algebra linear: exercícios e aplicações", McGraw-Hill
Note: we only know truly 1,2 and 5. There are plenty of books of Álgebra Linear in section M15 of the library.
Teaching Staff
- Joaquim Manuel Cunha Correia
- Manuel Baptista Branco [responsible]
Certificações
