DEPARTAMENTO DE FÍSICA

Linear Algebra and Analytical Geometry - F+EF

Ano letivo: 2017-2018

Specification sheet

Specific details

course code | cycle os studies | academic semester | credits ECTS | teaching language |

1001950 | 1 | 1 | 6 | pt |

Learning goals

Given the fact that this is the first formal contact students have with mathematical abstraction, the topics to be developed in this curricular unit require that different mathematical examples, that students are able to master, are presented and their generalizations in order to introduce the generic concepts of matrix, vector space and linear transformation. These are the mathematical tools that students will develop with the main objective of using them in other mathematical areas and apply them in Engineering (determinants, method of Gaussian elimination and the method of least squares in the resolution of linear systems, matrix diagonalization).

Generic competences in:

analysis and summary

organization and planning

oral and written communication

solve problems

critical thinking

communicate with people who are not specialists in the field

understand the language of other specialists

autonomous learning

apply the theoretical knowledge in practice

self-criticism and self-assessment

Generic competences in:

analysis and summary

organization and planning

oral and written communication

solve problems

critical thinking

communicate with people who are not specialists in the field

understand the language of other specialists

autonomous learning

apply the theoretical knowledge in practice

self-criticism and self-assessment

Syllabus

1. Matrices ? Operations with matrices.

2. Systems of Linear Equations - Method of Gaussian elimination.

3. Matrices inversion ? Gauss-Jordan Algorithm.

4. Determinants.

5. Vector Spaces.

6. Linear transformations.

7. Vector Spaces with Intern Product. ? The method of least square.

8. Matrix diagonalization.

9. Geometric applications in R2 and R3.

2. Systems of Linear Equations - Method of Gaussian elimination.

3. Matrices inversion ? Gauss-Jordan Algorithm.

4. Determinants.

5. Vector Spaces.

6. Linear transformations.

7. Vector Spaces with Intern Product. ? The method of least square.

8. Matrix diagonalization.

9. Geometric applications in R2 and R3.

Prerequisites

Knowledge and mastering of topics that were taught in Mathematics in High school.

Generic skills to reach

. Competence in analysis and synthesis;. Competence to solve problems;

. Critical thinking;

. Competence in applying theoretical knowledge in practice;

. Competence in organization and planning;

. Competence in oral and written communication;

. Competence to communicate with people who are not experts in the field;

. Competence in understanding the language of other specialists;

. Self-criticism and self-evaluation;

(by decreasing order of importance)

Teaching hours per semester

lectures | 45 |

theory-practical classes | 30 |

total of teaching hours | 75 |

Assessment

Sseminar or study visit | - % |

Laboratory or field work | - % |

Problem solving | 0 to 10 % |

Synthesis work thesis | - % |

Project | - % |

Research work | - % |

Mini tests | 0 to 20 % |

Assessment Tests | 0 to 90 % |

Exam | 0 to 100 % |

Other | - % |

- % | |

- % |

assessment implementation in 20172018

Assessment Problem solving ? 0% to 10%. Mini-tests ? 0% to 20%. Midterm tests ? 0% to 90%. Exam ? 0% to 100%.: 100.0%

Assessment Problem solving ? 0% to 10%. Mini-tests ? 0% to 20%. Midterm tests ? 0% to 90%. Exam ? 0% to 100%.: 100.0%

Bibliography of reference

Referências Principais

Ana Paula SANTANA, João QUEIRÓ (2010) Introdução à Álgebra linear.Trajectos Ciência, 10. Gradiva.

Seymour LIPSCHUTZ (1972) Álgebra linear, McGraw-Hill.

Referências Complementares

GOODAIRE, Edgar (2003). Liner Algebra: A Pure and Applied First Course. Prentice Hall, Pearson Education Inc.

LEON, Steven J. (2002). Linear Algebra with Applications. New Jersey: Prentice Hall.

MAGALHÃES, Luís T. (1989). Álgebra Linear como Introdução a Matemática Aplicada. Texto Editora.

STRANG, Gilbert (1988). Linear Algebra and its Applications, San Diego: Harcout Brace Jovanovich.

Ana Paula SANTANA, João QUEIRÓ (2010) Introdução à Álgebra linear.Trajectos Ciência, 10. Gradiva.

Seymour LIPSCHUTZ (1972) Álgebra linear, McGraw-Hill.

Referências Complementares

GOODAIRE, Edgar (2003). Liner Algebra: A Pure and Applied First Course. Prentice Hall, Pearson Education Inc.

LEON, Steven J. (2002). Linear Algebra with Applications. New Jersey: Prentice Hall.

MAGALHÃES, Luís T. (1989). Álgebra Linear como Introdução a Matemática Aplicada. Texto Editora.

STRANG, Gilbert (1988). Linear Algebra and its Applications, San Diego: Harcout Brace Jovanovich.

Teaching method

This curricular unit comprises:

(i) 45 hours of theoretical lecture classes.

(ii) 30 hours of theoretical and practical classes in which students are required to present to their classmates the solved exercises that were prepared at home.

(iii) the emergence of weekly tutorial classes (to clarify students? doubts).

Method of Assessment:

Problem solving ? 0% to 10%.

Mini-tests ? 0% to 20%.

Midterm tests ? 0% to 90%.

Exam ? 0% to 100%.

(i) 45 hours of theoretical lecture classes.

(ii) 30 hours of theoretical and practical classes in which students are required to present to their classmates the solved exercises that were prepared at home.

(iii) the emergence of weekly tutorial classes (to clarify students? doubts).

Method of Assessment:

Problem solving ? 0% to 10%.

Mini-tests ? 0% to 20%.

Midterm tests ? 0% to 90%.

Exam ? 0% to 100%.

Resources used