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Code: EEC0004     Acronym: ALGE

Classification Keyword
OFICIAL Mathematics

Instance: 2011/2012 - 1S

Active? Yes
Responsible unit: Department of Electrical and Computer Engineering
Course/CS Responsible: Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEEC 324 Syllabus (Transition) since 2010/2011 1 - 6 63 162
Syllabus 1 - 6 63 162

Teaching - Hours

Lectures: 0,00
Recitations: 4,00
Type Teacher Classes Hour
Recitations Totals 8 32,00
Fernando Arménio da Costa Castro e Fontes 8,00
José Nuno Teixeira de Almeida 12,00
Maria Paula Macedo Rocha Malonek 4,00
Abel Jorge Antunes da Costa 8,00

Teaching language



This course aims to provide concepts of Linear Algebra, which are of crucial importance to the training of the Electrical Engineering undergraduates. The fundamental concepts include algebraic structures, linear or vector distance, matrix analysis and linear transformations. This course aims to develop students' algebraic manipulation skills, analytical and independent reasoning and the ability to apply mathematical concepts to the resolution of practical problems.


1. Introduction to vectors
2. Matrixes
3. Gaussian method of elimination
4. Vector spaces
5. Linear transformations
6. Systems of linear equations
7. Projections and orthogonality
8. Determiners
9. Eigenvalues and eigenvectors
10. Bases changes
11. Applications

Mandatory literature

Notas a disponibilizar pelos docentes durante o Semestre (ver página da web)
Isabel Cabral, Cecília Perdigão, Carlos Saiago; Álgebra linear. ISBN: 978-972-592-309-2

Complementary Bibliography

Ana Paula Santana, João Filipe Queiró; INTRODUÇÃO À ÁLGEBRA LINEAR de , Gradiva, 2010. ISBN: 978-989-616-372-3
Gilbert Strang; Introduction to Linear Algebra, 4th Edition, Wellesley-Cambridge Press , 2009. ISBN: ISBN-10: 0980232716, ISBN-13: 978-0980232714
Gregório Luís e C. Silva Ribeiro; Álgebra Linear, McGraw-Hill.
Magalhães, Luís T.; Algebra linear como introdução à matemática aplicada
Jim Hefferon; Linear Algebra, 2008
Noble, Ben; Álgebra linear aplicada. ISBN: 85-7054-022-1
Noble, Ben; Applied linear algebra. ISBN: 0-13-041260-0
Strang, Gilbert; Linear Algebra and its Applications. ISBN: 0-12-673660-X

Teaching methods and learning activities

In theoretical classes important concepts and associated results will be presented, giving special emphasis to geometrical interpretations and their practical applications. Aiming to clarify the definitions and theorems presented, demonstrations will be given each and every time that these might help to achieve that understanding and the students will be given illustrative exercises to solve.
The theoretical-practical classes aim to better orientate the study of this course by making exercises that apply the taught information.
The practical classes are used to help the student solving exercises and to clarify their doubts.
The teachers of this course will also set a Schedule to receive the students beyond class time.


Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description Type Time (hours) Weight (%) End date
Attendance (estimated) Participação presencial 68,00
Teste 23,00 2012-02-10
Exame 1,50 2011-11-29
Exame 1,50 2012-01-25
Exame 2,00 2012-02-08
Total: - 0,00

Amount of time allocated to each course unit

Description Type Time (hours) End date
Estudo autónomo 66 2012-02-10
Total: 66,00

Eligibility for exams

Students are admitted to exams if:
- they are enrolled in the course
- they do not exceed the limit of absences (25% of theoretical-practical classes)
- they achieve a minimum average grade of 30% in microtests.

Students who have attended to the course in previous years and students with a special status will also be admitted to exams.

Calculation formula of final grade

Final mark (from 0 to 20) comprises two components:
FE- Final Exam (from 0 to 20)
CA- Continuous Assessment (from 0 to 20)

Continuous Assessment is based on four micro tests, which will take place at the theoretical-practical classes. Continuous Assessment grade will be the average grade of the four micro tests.

We will take into account the following situations to calculate the Final Mark:
- Situation 1- Students who are taking this course for the first time or who are repeating it, but are enrolled in the theoretical-practical classes.
For these students continuous assessment component will comprise four tests.
Final Mark:
FM= 0,3 * CA + 0,7 * FE

FM- Final Mark (from 0 to 20)
FE- Final Exam (from 0 to 20)
CA- Continuous Assessment (from 0 to 20)

Situation 2- Students who attend to the course in the previous year and who want to use their continuous assessment grade. These students have only to attend to the final exam.
Final Mark:
FM= 0,3 * CM + 0,7 * FE
FM- Final Mark (from 0 to 20)
FE- Final Exam (from 0 to 20)
CM- Previous year’s continuous assessment mark

Special assessment (TE, DA, ...)

Special Evaluation Students:
The students who, throughout the year, have the status either of working students or military personnel are dismissed from frequency and the compulsory distributed evaluation component. For these students, the evaluation in this course will be done with the final written exam, which will represent 100% of the final classification. Nevertheless, the students with these statuses that do the mini-test will be evaluated with it and with the final exam, with the proportion of 20% and 80%.

Students that attained frequency in 2003/2004:
The students who attended Algebra in 2003/2004 that had negative results but attained frequency (see grid) may, in concord with the general evaluation rules, be dismissed from attending classes this year. This also means that they don’t need to enrol on this year classes. Under those circumstances, the evaluation will be done only with the final exam, unless:
a) They do the mini-test, in which case they will be evaluated with it and the final exam, with the proportions of 20% and 80%.
b) They choose to keep the result of the distributed component of last year. This represents 20% of the final grade. These students must get in touch with the teacher by e-mail to sergio@fe.up.pt until December 19th, 2004.

Classification improvement

Classification improvement will be done with the final written exam. The result represents 100% of the final classification.


Language of instruction: Portuguese.
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