Publication in the Diário da República: Despacho nº 14433/2024 - 05/12/2024
5 ECTS; 1º Ano, 1º Semestre, 30,0 T + 30,0 TP + 4,50 OT , Cód. 912301.
Lecturer
- Maria Isabel Vaz Pitacas (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Not applicable.
Objectives
This course aims to foster inductive and deductive reasoning, equipping students with the ability to formulate problems in general contexts. It also seeks to develop proficiency in the use and manipulation of the symbolic language of Linear Algebra, which proves valuable across other courses within the degree programme. Students are expected to develop the following skills and competences:
1. Understand and grasp the concepts of Linear Algebra and its properties in order to develop rigorous reasoning and acquire the knowledge necessary for learning subjects in other units of the programme.
2. Apply knowledge and understanding: ability to relate concepts and model problems involving Linear Algebra; ability to apply Linear Algebra concepts in the modelling and resolution of problems related to Mechanical Engineering.
3. Make informed judgements: ability to apply critical thinking in the analysis of obtained results.
4. Develop communication skills: ability to use mathematical symbolism and achieve greater precision and clarity in both thought and expression.
5. Develop learning skills: ability to study and conduct research independently.
Program
1. Mathematical Logic
1.2. Designations and propositions.
1.3. Definition and properties of logical operations.
2. Matrices
2.1. General concepts and notation.
2.2. Matrix algebra.
2.3. Matrix representation and solution of systems of linear equations.
2.4. Characteristics of a matrix application to the discussion of a system of linear equations.
2.5. Inversion of a regular matrix Gauss-Jordan method.
2.6. LU decomposition.
3. Determinants
3.1. Definition of first and second order determinants.
3.2. Determinants of order n. Laplace's theorem.
3.3. Properties of determinants.
3.4. Applications of determinant theory.
4. Analytic geometry
4.1. Inner product of vectors, outer product and mixed product.
4.2. Analytical representation of a straight line.
4.3. Analytical representation of a plane.
4.4. Relative Position of Lines and Planes
4.5. Distances.
Evaluation Methodology
2 written tests (F1 and F2) marked classified from 0 to 20 and
Test 1 (T1) marked from 0 to 20 or
2 written tests(F1 and F2) marked from 0 to 20
Final grade=0.9x[(F1+F2)/2]+0.1xT1
or grade =(F1+F2)/2.E/or exam.
Bibliography
- Amaral, I. e Ferreira, M. (2009). Álgebra Linear 2º Vol Espaços Vetoriais e Geometria Analítica. Lisboa: Edições Sílabo
- Ferreira, M. e Amaral, I. (2008). Álgebra Linear 1º Vol Matrizes e Determinantes. Lisboa: Edições Sílabo
- Kolman, B. e Hill, D. (2014). Elementary Linear Algebra with applications. Reino Unido: Pearson Education Limited
- Monteiro, A. (2006). Álgebra Linear e Geometria Analítica. Lisboa: McGRaw-Hill
- Pitacas, I. (2025). Apontamentos de Álgebra Linear. Abrantes: ESTA
Teaching Method
Lectures (T) with presentation of the subject matter followed by illustrative examples, with exercises solved in theoretical-practical (TP) classes and clarification of doubts in tutorials (OT).
Software used in class
Productivity tools and elearning platforms.
