Linear Algebra

Code:

CVD001

Sigla:

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática e Informática

Ocorrência: 2023/2024 - 1S

Ativa?	Yes
Unidade Responsável:	Departamento de Matemática e Informática
Curso/CE Responsável:	Undergraduate in Civil Engineering

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
CIVD	18	Study Plan	1	-	5	75	135

Docência - Responsabilidades

Docente	Responsabilidade
Clara Sofia Gomes Carlos

Docência - Horas

Theorethical:	2,00
Practical and Laboratory:	2,00

Type	Docente	Turmas	Horas
Theorethical	Totais	1	2,00
Theorethical	José António da Silva Carvalho		2,00
Practical and Laboratory	Totais	1	2,00
Practical and Laboratory	José António da Silva Carvalho		2,00

Língua de trabalho

Portuguese

Objetivos

To acquire some calculus techniques which are widely used in other curricular units; among these techniques we highlight matrix techniques, representation of linear equation systems and their resolution, determinants and their applications as well as linear spaces and linear transformations.

Resultados de aprendizagem e competências

Not applicable.

Modo de trabalho

Presencial

Programa

Matrices: Definition. Special matrices. Algebraic operations with matrices. Classification of matrices according to their properties. Linear combination of rows and columns of a matrix. Linear (in)dependence of rows and columns of a matrix. Matrix equations. Gauss elimination. Rank of a matrix. Matrix Inverse and its properties.
Determinants : Definition. Sarrus rule. Determinant calculus via triangular factorization. Adjoint matrix. Solution of linear systems using Cramer’s rule. Linear spaces Revisions of vector calculus
Linear spaces:Linear combination, linear (in)dependence, generators, basis and dimension. Linear subspaces
Linear transformations:Linear transformations and their properties. Kernel and image space. Generators,bases and dimension of kernel and image spaces.
Eigenvalues and eigenvectors: Characteristic polynomial. Calculation of eigenvalues and eigenvectors
Inner, outer and mixed product: Definition and geometric interpretation. Properties.

Bibliografia Obrigatória

L. Magalhães; Álgebra Linear, como Introdução a Matemática Aplicada, Texto Editora
F. R. Dias Agudo; Introdução à Álgebra Linear e Geometria Analítica,, Livraria Escolar Editora

Bibliografia Complementar

S. Lang; Introduction to Linear Algebra, Springer
G. Strang; Linear Algebra and Its Applications, Academic Press

Métodos de ensino e atividades de aprendizagem

Theoretical classes with lecturing periods with application examples followed by small tasks to be done by the students in order to consolidate the contents previously taught. Practical classes dedicated to problem solving, individually or in small groups.

Continuous assessment through two written tests.
Final assessment through a written exam.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	75,00
Frequência das aulas	60,00
Total:	135,00

Obtenção de frequência

Not applicable

Fórmula de cálculo da classificação final

Continuous assessment

1/2*test1+1/2*test2

Minimum test score of 6.

Final assessment

100% exam

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