Base Knowledge
Main properties of the real number system and the complex number system (taught in high school mathematics subjects)
Teaching Methodologies
Theoretical classes consist of a detailed exposition of each subject that is immediately complemented by the resolution of exercises. In the theoretical-practical classes it is intended that the student solves application exercises with the guidance of the teacher.
Learning Results
Objectives: To provide students with basic knowledge of Linear Algebra, with a view to easy application of the discipline in the most diverse fields of Engineering.
Skills: Development of mathematical abstraction and logical reasoning, as well as identification, understanding and solving problems involving matrix calculus (matrices, linear systems, determinants), vector spaces and eigenvalues and eigenvectors (diagonalization of matrices).
Program
CHAPTER I – Reviews on complex numbers
CHAPTER II – Matrices
Definitions
Operations with matrices and properties
CHAPTER III – Systems of Linear Equations
Condensation of matrices and characteristic
Systems of linear equations
Classification and solution of systems of linear equations by condensation
Inverse matrix
CHAPTER IV – Determinants
Definitions, evaluation and Properties
Laplace’s Theorem
Cramer’s Rule
CHAPTER V – Vector Spaces
Definitions and examples
Vector subspaces
Vector subspace generated by a set of vectors
Linear dependence and independence
Basis and dimension
CHAPTER VI – Eigenvalues and Eigenvectors
Definitions, computation and properties
Diagonalization
Cayley-Hamilton Theorem
Curricular Unit Teachers
Internship(s)
NAO
Bibliography
- Anton, H. & Rorres, C. (2005). – Elementary Linear Algebra with applications. (9ª ed.). John Wiley & Sons.
- Cabral, I., Perdigão, C. & Santiago, C. (2018). Álgebra Linear – Teoria, Exercícios resolvidos e Exercícios propostos com soluções. (5ª ed.). Escolar Editora.
- Fidalgo, C. (2016). – Álgebra Linear, DFM, Instituto Superior de Engenharia de Coimbra.
- Graham, A. (2018). Matrix Theory and Applications for Scientists and Engineers. Dover Books on Mathematics
- James, G. & Dyke, P. (2020). Modern Engineering Mathematics. (6ª ed.). Pearson.
- Kreyszig, E. (2011). Advanced Engineering Mathematics (10ª ed.). John Wiley & Sons.
- Monteiro, A., Marques, C. & Pinto, G. (2000). Álgebra Linear e Geometria Analítica. Problemas e Exercícios. McGraw-Hill.
- Nicholson, W. (1993). Elementary Linear Algebra with Applications. (2ª ed.). PWS Publishing Company.
- Santana, A. & Queiró, J. (2018). Introdução à Álgebra Linear. Gradiva.