Algebra

Code:

L.EEC002

Acronym:

ALG

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EEC	286	Syllabus	1	-	6	52	162

Teaching language

Portuguese

Objectives

The aim of this course is to endow the students with a solid body of fundamental knowledge in linear algebra so as to promote its application in the solution of engineering problems. The concepts and methods studied in the course are to be completed with examples of basic applications in electrical engineering in order to facilitate their future use both during the study and in a professional environment. Moreover, the students are encouraged to develop the capacity of critical analysis together with the ability of applying the concepts and techniques learnt in this course to the solution of practical engineering problems. This course will also enable the students to carry out an autonomous study of more advanced linear algebra concepts and techniques that might be necessary in the framework of their academic training and/or in their future professional activity.

Learning outcomes and competences

After this course the students are expected to master the concepts and techniques specified below, which constitute the foundations of Linear Algebra.
They are also espected to dormulate and solve problems using these concepts.

Working method

Presencial

Program

• Matrices and determinants (matrix operations, inverse matrix, elementary row/column operations; determinants, definition, properties, computation, application to matrix inversion; matrix rank)                    


• Systems of linear equations (matrix formulation; the Gauss-Jordan method for the study and computation of the solutions of systems of linear equations)                    


• Vectors in the plane and in the three-dimensional space (operations, reference frames, translation and rotation transformations, inner product, vector product; geometry in R² and in R³)

•  Real vector spaces (definition and properties; linear subspaces; generators, linear independence, bases, dimension; coordinates, change of basis)

• Real Euclidian spaces (inner product, norm, distance; orthogonality, orthonormal bases, orthogonal projections and applications)

• Linear transformations (definition, properties, matrix representation, kernel and range, injective and surjective maps, the dimensions theorem).

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

The course contact hours are as follows: 2 hours of lectures (2T) and 2 hours of exercise classes (2TP) per week, during 12 weeks. The lectures can be divided either in two sessions of 1 hour each.

In the lectures, important concepts and 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 their understanding. Illustrative examples will always be presented.

In order to consolidate the concepts and techniques taught in the lectures and, simultaneously, to promote their autonomy, the following method will be adopted for the exercise classes. The students are encouraged to autonomously solve a number of proposed problems prior to each session. During the exercise classes the students’ problem solutions are checked and questions regarding these solutions (or any other related subject of the course) are clarified.

Type of assessment: By means of quizzes/homeworks (30%) and a final test during the semester (70%); no final exam.

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Teste	70,00
Trabalho escrito	30,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

In order to be admitted to the tests/exams, students must fulfill all the following conditions:
   - be enrolled in the course;
   - do not exceed the limit of absences from the exercise classes (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 CU, 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 doing the quizzes and/or homeworks to be handed in during the semester as well as a final test . If a student is not approved in this evaluation, he/she still can still resit in the exam.


The FINAL CLASSIFICATION in the CU will be (on a scale of 0 to 20) corresponds to:

• 0.7 x (mark of the final test) + 0.3 x (mark obtained in the quizzes and/or homeworks to be handed in)

or

• The classification in the resit exam (E), (maximum score 20).

Important Notes:
    a) the marks obtained in the evaluation components do not remain valid for subsequent years;
    b) If a student fails to do one of the evaluation components, the score on this component, 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 CU approval may be obtained by doing the already mentioned evaluation components during the semester 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.