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Code: | EIC0003 | Acronym: | ALGE |

Keywords | |
---|---|

Classification | Keyword |

OFICIAL | Mathematics |

Active? | Yes |

Responsible unit: | Mathematics Section |

Course/CS Responsible: | Master in Informatics and Computing Engineering |

Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|

MIEIC | 167 | Syllabus since 2009/2010 | 1 | - | 4,5 | 56 | 121,5 |

Teacher | Responsibility |
---|---|

António Joaquim Mendes Ferreira |

Lectures: | 2,00 |

Recitations: | 2,00 |

Type | Teacher | Classes | Hour |
---|---|---|---|

Lectures | Totals | 1 | 2,00 |

António Joaquim Mendes Ferreira | 2,00 | ||

Recitations | Totals | 6 | 12,00 |

António Joaquim Mendes Ferreira | 12,00 |

SPECIFIC AIMS: This discipline has two main objectives: the promotion of logical reasoning and methods of analysis and the introduction and theoretical development of a set of concepts that will be fundamental to support the study of other disciplines along this course of studies.

LEARNING OUTCOMES: Learning Outcomes: At the end of the semester, students should be: 1. capable of analysing and solving systems of linear equations; 2. acquainted with basic matrix operations and its properties; 3. capable of defining a non-singular matrix and be acquainted with the properties of an inverse matrix and its calculation; 4. capable of defining the determinant of a matrix and be acquainted with its properties and calculation; 5. capable of defining vector space, vector subspace and Euclidian space; 6. capable of defining linear combination of vectors, linear independence/dependence vectors and subspace; 7. capable of defining and determining a base and the dimension of a vector space; be capable of obtaining the components of a vector in relation with its base; 8. capable of defining a linear transformation and calculate and characterize its kernel; be acquainted with algebraic operations and define and calculate inverse transformation; 9. capable of using a matrix to represent a linear transformation and operate linear transformations using matrix algebra; 10. capable of defining a change of base matrix and apply it to problems of change of base that involve elements of a vector space and linear transformations; 11. capable of defining similar matrices and be acquainted with their properties; 12. capable of calculating eigenvalues and eigenvectors of linear transformations and to be acquainted with their properties, and if possible identify a diagonal matrix representation for a linear transformation.

Basic knowledge of systems of equations and vector algebra

Definition of vector space Vector subspaces Linear dependence and independence Bases and dimension Components Inner product Euclidian spaces Norms and orthogonality Linear spaces of matrices Product of matrices Transposed matrix Inverse matrix Square matrix Orthogonal matrix Similar matrices Change of bases matrices Determinants Condensation method and Laplace theorem Inversion of matrices using a determinant Systems of linear equations Gaussian method of elimination Cramer’s rule Linear transformation Kernel Algebraic operations with linear transformations Injective linear transformations Matrix representation of a linear transformation Isomorphism between linear transformations and matrices Eigenvalues and eigenvectors of linear transformations Characteristic polynomial Conditions for the existence of diagonal matrix representation and linear transformation

Apostol, Tom M.; Calculus. ISBN: 84-291-5001-3

Barbosa, José Augusto Trigo; Noções sobre matrizes e sistemas de equações lineares. ISBN: 972-752-069-3 972-752-065-0

J.A. Trigo Barbosa; ALGA - Apontamentos Teórico-Práticos

J.A. Trigo Barbosa, J.M.A. César de Sá, A.J. Mendes Ferreira; ALGA - Exercícios Práticos

Ribeiro, Carlos Alberto Silva; Álgebra linear. ISBN: 972-8298-82-X

Monteiro, António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8

Theoretical classes: detailed exposition of the program of the discipline illustrated by application examples. Theoretical-practice classes: application of the theoretical concepts in the resolution of several exercises that can be found in the proposed literature.

Designation | Weight (%) |
---|---|

Exame | 100,00 |

Participação presencial | 0,00 |

Total: |
100,00 |

Designation | Time (hours) |
---|---|

Estudo autónomo | 66,00 |

Frequência das aulas | 56,00 |

Total: |
122,00 |

According to General Evaluation Rules of FEUP

Students have to attend to three mini-tests. Final mark will be based on the average mark of the three exams. The dates of the mini-test and the final exam have not yet been set. The exams are closed book exams.

Students have to attend to three mini-tests. Final mark will be based on the average mark of the three exams. The dates of the mini-test and the final exam have not yet been set. The exams are closed book exams.

Not applicable

Although working students are exempt from classes, they must do the mini-tests

During the final mini-test, students can improve the first and second mini-test.

Students are not allowed to use a graphics calculator on the exam.

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Page generated on: 2019-03-21 at 23:13:23

Page generated on: 2019-03-21 at 23:13:23