| Code |
14329
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Mathematics A (Secondary Education of the Science and Technology Course)
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Learning outcomes |
The main objective of this curricular unit is to make the student acquire a strong and secure domain of the main tools and methods of an introductory course to Linear Algebra, enabling its use, in a pure or/and applied way. The UC also consists of an introduction to the concepts of Analytical Geometry.
Experimental skills complementary to the traditional method of studying content are introduced (eg use of software), helping in the comprehensive learning of mathematical facts, concepts and principles.
The Student should be able to apply the knowledge in solving problems related to his/her training area and which are used throughout his/her academic and professional path.
The syllabus, defined based on the objectives, fit into the contents usually taught in similar curricular units at other European Universities, namely Portuguese.
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Syllabus |
Chapter 1. Matrices: Types of matrices; Operations with matrices; Rank of a matrix; Inverse of a matrix; Systems of linear equations.
Chapter 2. Systems of Linear Equations
Chapter 3. Determinants: Determinant of a square matrix; Adjoint matrix and inverse matrix; Application to linear systems of equations;
Chapter 4. Vector Spaces: Definition of vector space; Subspaces; Linear combinations and spanning set; Linear dependence and independence; Basis and dimension of a vector space;
Chapter 5. Linear Transformations: Definition and examples; Properties; Matrix of a linear transformation; Change of basis matrix;
Chapter 6. Eigenvalues and eigenvectors of a matrix; Similar matrices; Diagonalizable matrices;
Chapter 7. Inner product spaces: Inner product, Norm; Cauchy–Schwarz inequality; Orthogonality, orthonormal basis and Gram-Schmidt orthogonalization process. Vector cross product and the scalar triple product of vectors.
Chapter 8. Plans and Lines.
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Main Bibliography |
1) Isabel Cabral, Cecília Perdigão, Carlos Saiago, "Álgebra linear: teoria, exercícios resolvidos e exercícios propostos com soluções", Escolar Editora, 4ª edição, 2014.
2) Álgebra linear e geometria analítica, according to the lesson Prof. Doutor Sampaio Martins e do Prof. Doutor Paulo Rebelo.
3) F. R.Dias Agudo, "Introdução à Álgebra linear e geometria analítica", Escolar Editora
4) Introdução à Álgebra Linear, Reginaldo J. Santos (http://gradmat.ufab.edu.br/disciplinas/listas/alglin/gaalt00.pdf)
5) Luís T. Magalhães, "Álgebra linear como introdução à matemática aplicada", Escolar Editora, 2001.
6) Howard Anton, "Álgebra linear com aplicações"
7) Seymour Lipschutz, "Álgebra linear: resumo da teoria, 600 problemas resolvidos, 524 problemas propostos"
8) Material made available in Moodle & Central Library in section M-2.4
9) Evar D. Nering & John Wiley, "Linear Algebra And Matrix Theory", New York, 1970
10) Howard Anton & Robert Busby, "Álgebra Linear Contemporânea", Bookman, 2006
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Teaching Methodologies and Assessment Criteria |
The teaching-learning methodology is centered on the student, who, throughout the semester, acquires and applies the concepts, with their autonomous work. In this way, particular importance is given to continuous assessment, which allows the student, throughout the semester, to demonstrate in stages the skills acquired through his/her work. To this end, two frequencies are planned.
The student must demonstrate, at the end of the semester, that he/she has acquired a minimum of competences in order to be admitted to the exam. It is possible that you will be admitted to the exam if you have demonstrated to the teaching team that you have acquired the minimum skills.
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Language |
Portuguese. Tutorial support is available in English.
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