Algebra

Code:

EEC0004

Acronym:

ALGE

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 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	245	Syllabus	1	-	6	63	162

Teaching language

Portuguese

Objectives

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 matrix analysis, vector spaces 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.

Learning outcomes and competences

At the end of this course students are expected to master the following concepts and techniques:
- Concept of matrix;
- Matrix manipulation techniques;
- Application of matrices to the representation, classification and solution of linear equation systems;
- Determinants (concept, computation techniques, and applications) ;
- Concept of vector space;
- Relation between vector spaces, matrices and systems of linear equations;
- Concept, calculation and application of vector projections (e.g., orthogonal bases obtaining);
- Concept and matrix representation of linear transformations;
- Concept and calculation of eigenvalues and eigenvectors.

Working method

Presencial

Program

1. Systems of Linear Equations and Matrixes;
2. Determiners;
3. Vector Spaces;
4. Projections and Orthogonality;
5. Linear Transformations;
6. Eigenvalues and Eigenvectors.

Mandatory literature

Notas a disponibilizar pelos docentes durante o Semestre (ver página da web)

Complementary Bibliography

Ana Paula Santana, João Filipe Queiró; INTRODUÇÃO À ÁLGEBRA LINEAR de , Gradiva, 2010. ISBN: 978-989-616-372-3
Isabel Cabral, Cecília Perdigão, Carlos Saiago; Álgebra linear. ISBN: 978-972-592-309-2
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 the lectures important concepts and associated results will be presented, giving special emphasis to their practical applications. In order to clarify the definitions and theorems presented, proofs will be given each and every time that these might help to achieve that understanding and the students will be given illustrative examples.

The exercise classes aim to better orientate the study of this course by presenting exercises that apply the taught information and helping the students solve these exercises and to clarify their doubts.

The lecturers of this course will also set office hours to receive the students.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	94,00
Frequência das aulas	68,00
Total:	162,00

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 the exercise classes).

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

To get a final classification, in the UC, a student must satisfy the attendance requirement ("frequency") or be excused from obtaining it (see above, under "Obtaining frequency"). Under these conditions, students can be approved by writing three tests and/or a final exam. If a student is not approved by tests, he/she still can still resit in the exam.
This means that there are four different evaluation elements namely:
     1) First Test (T1) to be held on the day, time and room to be determined;
     2) Second Test (T2) to be held on the day, time and room to be determined;
     3) Third Test (T3) to be held on the day, time and room to be determined;
     4) Resit Exam (E) to be marked by the services.

Test T1 will count for 5 values and tests T2 and T3 for 7,5 values each. The following minimum scores must be achieved 3,50 (out of 5+7,5=12,5) in tests T1 and T2 (taken together); T3 - 2,50 (out of 7,5). In order to be approved in the normal evaluation period, students must attain the minimum scores in the tests, together with the final classification of 10 (9,50) out of 20.

The FINAL CLASSIFICATION in the UC will be (on a scale of 0 to 20) corresponds to:
     - The sum of the marks obtained in T1, T2 and T3 (maximum total score of 5+7,5+7,5=20), or
     - The classification in the resit exam (E), (maximum score 20).

Important Notes:
    a) the marks obtained in the tests do not remain valid for subsequent years;
    b) If a student fails to attend one of the tests, the score of this test, to be considered in the calculation of final classification, is zero.

Special assessment (TE, DA, ...)

Students who are under special statutes (TE, DA, ...) during the current academic year, are exempt from frequency. The UC approval may be obtained by doing the tests (T1, T2 and T3) or the resit exam (E). The calculation of the grade is identical to that described above.

Classification improvement

Classification improvement will be done with a written exam (resit period). The result corresponds to 100% of the final classification.

Observations

Language of instruction: Portuguese.