| Code |
8535
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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 of High School (10.º, 11.º, 12.º)
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Mode of delivery |
Face-to-Face
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Work placements |
Not applicable
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Learning outcomes |
The curricular unit is an introduction to Linear Algebra. It is intended to develop mathematical, logical, critical and analytical reasoning and student’s autonomy when formulating and solving problems. Concretely, at the end of the curricular unit, the student should be able to: make operations over/with matrices and apply properties; determine the rank of a matrix; classify and solve, using matrices, systems of linear equations; apply properties of the inverse of a regular matrix and determine it; calculate the determinant of a square matrix and apply properties; solve problems of Analytic Geometry; identify/sketch quadric surfaces; decide the linear independence/dependence of vectors; characterize a spanned subspace; determine the dimension of a linear space; represent a linear application by a matrix; calculate eigenvalues and eigenvectors, and apply properties; interpret and use mathematical language.
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Syllabus |
0: Motivation.
1: Matrices and Systems of Linear Equations
Real and complex matrices. Matrix operations. Elementary operations.
Resolution of systems of linear equations. Inverse of a matrix.
2: Determinants
Determinant of a square matrix, properties; Laplace's theorem. The Adjoint and the inverse of
a matrix; Application to systems of linear equations;
3: Vector Spaces
Definition of vector space. Subspaces.
Linear Combinations. Linear independence and dimension.
4: Linear Transformations
Definition and examples. Properties. Matrices and linear transformations.
5: Eigenvalues and eigenvectors of a matrix.
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Main Bibliography |
Anton, H., & Busby, R. C. (2006). Álgebra Linear contemporânea. Bookman.
Cabello, J. G. (2006). Álgebra Lineal. Delta.
Cabezón, E. S. de. (s. d.). Las matemáticas son para siempre. https://www.ted.com/talks/eduardo_saenz_de_cabezon_math_is_forever?language=es&subtitle=pt
Cabral, I., Perdigão, C., & Saiago, C. (2021). Álgebra Linear. Escolar.
Dias Agudo, F. R. (1996). Introdução à Álgebra Linear e Geometria Analítica. Escolar.
Lay, D. C. (2012). Álgebra Linear e suas aplicações. LTC.
Lipschutz, S. (1972). Álgebra linear. McGraw-Hill.
Magalhães, L. T. (2001). Álgebra Linear como introdução à Matemática Aplicada. Texto.
Nering, E. D. (1970). Linear Algebra and Matrix Theory. John Wiley & Sons.
Rose, Tony de. (2014). Pixar: The math behind the movies. https://www.youtube.com/watch?v=_IZMVMf4NQ0
Santana, A. P., & Queiró, J. (2010). Introdução à Álgebra Linear. gradiva.
Strang, G. (1976). Linear Algebra and its applications. Academic.
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Teaching Methodologies and Assessment Criteria |
The methodology is student-centered, and the student is expected, during the semester, to acquire and apply the concepts through autonomous work. In this sense, the periodic assessment, which allows the student to show the acquired skills, is paramount. More concretely, three written tests will take place.
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Language |
Portuguese. Tutorial support is available in English.
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