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# Linear Algebra and Analytical Geometry

 Code 8620 Year 1 Semester S1 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements Mathematics 12th grade Mode of delivery Face to face Work placements There are no work placement Learning outcomes At the end of the curricular unit, the student should be able to:- Compute the sum, the product, and the transpose of a matrix;- Compute the rank of a matrix;- Identify an invertible matrix and compute its inverse;- Solve and classify systems of linear equations;- Identify subspaces of a vector space and compute a base;- Compute the matrix of a linear transformation;- Solve systems of linear equations and compute the inverse of a matrix using determinants;- Compute the eigenvalues of a matrix;- Identify the most important properties of an inner product and vectorial product. Syllabus 0: Motivation for Linear Algebra1: Matrices and Systems of Linear EquationsReal and complex matrices. Matrix operations. Elementary operations.Resolution of systems of linear equations. Inverse of a matrix.2: DeterminantsDeterminant of a square matrix, properties; Laplace's theorem. The Adjoint and the inverse of a matrix; Application to systems of linear equations;3: Vector SpacesDefinition of vector space. Subspaces.Linear Combinations. Linear independence and dimension.4: Linear TransformationsDefinition and examples. Properties. Matrices and linear transformations.5: Eigenvalues and eigenvectors of a matrix.6: Analytical GeometryVector calculus: inner product and vectorial product; Main Bibliography Boulos, P., Camargo, I. (1987), Geometria Analítica, McGraw-Hill.Cabello, J. (2006), Álgebra Lineal, Delta.Cabral, I., Perdigão, C., Saiago, C. (2009), Álgebra Linear, Escolar.Dias Agudo, F. R. (1992), Introdução à Álgebra Linear e Geometria Analítica, Escolar. Khoury, J. (s. d.), Applications to Chemistry, \url{http://aix1.uottawa.ca/~jkhoury/chemistry.htm}Lay, D. C. (2005), Álgebra Linear e suas aplicações, LTC.Lipschutz, S. (1972), Álgebra Linear, McGraw-Hill.Magalhães, L. T. (1989), Álgebra Linear como introdução à matemática aplicada, Texto.Santana, A. P., Queiró, J. (2018), Introdução à Álgebra Linear, gradiva.Santos, R. (2010), Álgebra Linear, http://www.mat.ufmg.br/~regi/livros.html 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, two written tests and two group tasks will take place. Language Portuguese. Tutorial support is available in English.

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Industrial Chemistry
Last updated on: 2021-10-15

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