Description

Theory
2

Theory/Practice
2

Instructors

Amélia Caldeira

Contents

1- MATRICES
1.1 Definition and representation of a matrix
1.2 Matrix operations and properties
1.3 Elementary row and column operations
1.4 Matrix condensation
1.5 Rank of a matrix; computation using Gaussian Elimination Method (GEM)
1.6 Inverse matrix
1.7 Matrix equations
1.8 Applications
 

2 - DETERMINANTS
2.1 Definition and properties
2.2 Laplace?s Theorem. Calculation of determinants of order n
2.3 Applications
 

3 - SYSTEMS OF LINEAR EQUATIONS (SLE)
3.1 Definition and matrix form of a system of linear equations
3.2 Classification and solution of systems with parameters
3.3 Cramer?s systems and homogeneous systems
3.4 Applications
 

4 - REAL VECTOR SPACES
4.1 Definition and properties
4.2 Vector subspaces
4.3 Basis and dimension
 

5 - LINEAR TRANSFORMATIONS
5.1 Definition and properties
5.2 Matrix representation
5.3 Kernel and image
5.4 Eigenvalues and eigenvectors
 

6 - ANALYTIC GEOMETRY
6.1 Dot product and cross product
6.2 Equations of lines and planes
6.3 Topological and metric problems

Learning Outcomes

GENERAL OBJECTIVES
The aim is for students to:
(P1) complement and consolidate their mathematical background acquired throughout their learning process;
(P2) develop their reasoning and abstraction skills;
(P3) cultivate mathematical thinking and acquire critical thinking skills;
(P4) become capable of applying mathematical techniques that are essential for understanding and interpreting topics taught in other undergraduate course units and fundamental to engineering.

SPECIFIC OBJECTIVES
Specifically, by the end of the semester, students should be able to:
(O1) perform basic matrix operations and understand their properties; define and determine the rank of a matrix and compute the inverse matrix; solve matrix equations;
(O2) compute determinants and manipulate them using their properties;
(O3) analyse and solve systems of linear equations;
(O4) identify and construct real vector spaces and work with vectors, particularly to verify whether they can be used as a basis of a vector space;
(O5) identify linear transformations, determine the associated matrices, and compute their eigenvalues and eigenvectors;
(O6) understand and apply the concepts of Euclidean spaces, including their definition and identification of examples, as well as compute norms, distances, and angles; apply the cross product and the scalar triple product in solving problems related to lines and planes. Topological and metric problems