ISLA IPGT 2091

Linear Algebra

• ApresentaçãoPresentation

  The main objective of this course is to provide students with fundamental knowledge in the field of Algebra and logical and mathematical reasoning. It is intended that, through various theoretical and practical strategies, students can apply and solidify the knowledge acquired throughout the semester on operations and fundamental structures, matrices, determinants, systems of linear equations, vector spaces and vectors and eigenvalues .
• ProgramaProgramme

  Fundamental operations and structures Cartesian product Binary interface Equivalence ratio Order relationship Groups, semigroups and groups Subgroups, Finite Groups Lagrange's theorem. Rings, Ring with unit Euler's theorem Bodies Matrices and Systems Matrix calculation Transposed from a matrix Gauss form Inverse matrix Systems of linear equations Determinants Calculation of order 2 and order 3 determinants Rule of Sarrus Laplace's rule Determinants properties Cramer's Rule Vector spaces Vectors and operations. Definition and properties Linear combination Linear dependence and independence Vector subspace Base and dimension of a vector space Change of base. Vectors and eigenvalues Definition Properties Diagonalization Applications
• ObjectivosObjectives

  At the end of the course, the student should be able to: Perform basic matrix calculation operations. Use matrix theory to study and solve systems of linear equations. Apply the techniques of linear algebra in analytical geometry. Interpret and apply the concepts associated with vector spaces and their own values ¿¿and vectors. Recognize the importance of algorithms in the applications of linear algebra. He must also have developed the capacity for abstraction and demonstration.
• BibliografiaBibliography

  Gomes, C. (2022). Material de Apoio à Unidade Curricular de Álgebra. ISLA-Instituto Politécnico de Gestão e Tecnologia. Magalhães, Luis T., Álgebra Linear: como Introdução a Matemática Aplicada, Texto Editora, 1993 Meyer, Carl D., Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, 2000 Monteiro, A., Álgebra Linear e Geometria Analítica, McGraw-Hill, 2001 Magalhães, L., Álgebra Linear como Introdução à Matemática Aplicada, Texto Editora, 1992
• MetodologiaMethodology

  Use of moodle where the student has access to digital sebentas that allows him to absorb the content through the virtual medium and when arriving at the classroom is already aware of the subject to be developed. The "inverted classroom" makes it possible to know the concepts before approaching them allowing to monetize the time of learning. Use of applications (PhotoMath, Maple Calculator, Microsoft Math Solver ...) that, in real time, allow the student not only to acquire knowledge but also to support their study. Use of the interactive whiteboard to make presentations more dynamic. Use of platforms (such as Zoom) to allow students who cannot be in person not to miss the possibility of integrating the class.
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  5
• NaturezaNature

  Mandatory
• EstágioInternship

  Não