(School year 2020/2021)


1. Identification and allocation of the Curricular Unit

School

Escola de Ciências e Tecnologia

Department

Matemática

Course code

5054

Course denomination

Mes. Int. em Engenharia Eletrotécnica e de Computadores

Curricular Unit code

106

Curricular Unit denomination

Álgebra linear e geometria analítica


Teacher in charge

Name

Category

Maria da Graça Pereira Soares

Professor Auxiliar


Other teachers from Curricular Unit

Names

Categories

Maria da Graça Pereira Soares

Professor Auxiliar



2. General information

Teaching load / contact hours / ECTS

Autonomous work (hours)

Distribution of contact hours

Total (hours)

ECTS

97.50


162

6.00


Schedule of classes

1º semestre:
T  turma 1
Monday at 14h00m with duration of 02h00m
TP  turma 1
Monday at 09h00m with duration of 02h00m


Hours to students attendance

Maria da Graça Pereira Soares  1º Semester 
Begin 
Duration 
Location 
From 
To 
Segunda, 11h00 
01h00 
F1.19 
28/10/2020 
30/01/2021 
Sexta, 11h00 
02h00 
F1.19 
28/10/2020 
30/01/2021 



3. Objectives, syllabuses and teaching methods

Curricular Unit objectives and skills to develop (max. 1000 characters)

The techniques presented in this course have as an objetive to develop the capacities of abstraction and logicaldeductive reasoning of students. It is intended that after the approval in this course the student has the ability:
To perform calculations with matrices and determinants.
To discuss and solve systems of linear equations using GaussJordan method, Cramer rule or the inverse of the simple matrix of the system
To recognize the concepts of vetor space (subspace, sum subspace, intersection subspace, bases) and linear application (kernel, image and matrix of a linear application) and use them to solve some related problems.
To determine eigenvalues and eigenvectors of a matrix as well as to investigate if a given matrix is diagonalizable.
To investigate if a given basis is ortogonal and/or all the elements of the basis gave norm 1.
It is intended that the student, at the end of the semester, could be able to do matricial calculus easily.

Syllabus (max. 1000 characters)

Solving linear systems, matrices, elementary operations, Gaussian elimination method. Characteristic of a matrix. Algebraic properties of matrices. "Special" matrices. Elementary matrices.Transposed matrix. Inverse of a square matrix. Resolution of linear systems using the inverse of a matrix.
Determinants: definition and properties. Laplace's theorem and Cramer's rule. Eigenvalues and eigenvectors. Adjoint matrix.
Vector spaces. Vector Subspaces. Linear dependence and independence. Bases and dimension. Subespace Sum; Intersection; Reunion of subspaces.
Linear applications. Kernel an image set. Algebraic operations with linear applications. Matrix representation of linear application. Isomorphism between linear transformations and matrices. Necessary and sufficient condition for the existence of diagonal matrix representaing a linear transformation.
Inner product and external product, mixed product. Norm. Orthogonal projection. Orthogonalization of GramSchmidt.

Planning teaching activity (according to school Schedule)  (optional)

_

Demonstration of the Curricular Unit syllabus coherence with the intended learning outcomes (max. 1000 characters)

It is intended that at the end of the course the students get skills involving the concepts and calculation of matrices, determinants, vector spaces and linear applications. For students succeed to achieve these objectives, the program contents were thought in order to cover the concepts necessary to understand the basics ones and also to cover the techniques and tools needed for the listed skills be acquired by the students.

Teaching / learning methodologies used (working methods, Curricular Unit running, resources, etc..) (max. 1000 characters)

The course is formally separated into two main components: theoretical and theoreticalpractical classes.
In the theoretical classes, definitions will be presented in a consistent and rigorous way, so that students can acquire as much as possible, a scientific maturity and thereby can be able to relate the various concepts studied, as well as their application in the theoretical and practical context. Afterwards, these concepts will be supported by examples and by solving some exercises. Moreover, it is essential to encourage students to actively participate with questions and / or relevant doubts so that they can develop their critical thinking and mathematical reasoning for questions arised not only in classes but also in the daytoday. In theoreticalpractical classes some questions are presented and some problems are proposed in order for students to solve and in this way enhance the knowledge acquired in the theoretical classes.

Demonstration of the consistency of teaching methodologies with the objectives of the Curricular Unit (max. 3000 characters)

The aim of this curricular unit is to provide students with the basic techniques in Linear Algebra. In this way, it becomes necessary to expose in a clear and coherent manner all the notions related to the objectives of this curricular unit, always taking into account the scientific accuracy that is required by this science. The exhibition will be made in theoretical classes. The exposed concepts will be later complemented by the resolution of problems in the practical classes. With these classes, it is intended that students can solve by themselves the proposed problems in order to enhance their knowledge.

4. Evaluation Methodology

Assessment modes, need to register prior to testing and transition conditions between modes

The evaluation is done according to the Pedagogical Norms of the University of TrasosMontes and Alto Douro.
Thus, students must be registered in SIDE on Theoretical (T) and theoreticalpractical classes (TP).
There are three independent modes of evaluation in the Course:
Mode 1: Continuous evaluation
Mode 2: Continuous evaluation followed of complementary evaluation;
Mode 3: Evaluation by Examination
Students who did not obtain approval on assessment mode, can make the proofs of the the second mode of evaluation.
All the students that meet the minimum criteria for admission to examination referred to in this form of UC, can submit to the third mode of assessment.

Minimum criteria for admission to examination

To have access to any written evaluation test, students must attend a minimum of 70% of contact hours (theoretical classes and practical classes) summarized.

Description of evaluation methods, respecting the Article 13 of Chapter IV of UTAD's Pedagogical Regulation (including, scheduling and calculation method).

The continuous evaluation and periodic (mode 1) shall consist of two written examinations of mandatory status (of equal weight in the weighting of the final grade) to be held on
1st test: 27 november of 2020
2nd test: 29 january of 2021
Every student will be considered approved in this course and exempt from any complementary evaluation if obtains
an average in the second test great or equal to 6 values
and
an average grade in the two tests great or equal to 9.5 values.
If the student obtains in the second test a grade greater than or equal to 6, he may repeat in the first call only one of the parts. The final grade will be the average of the two classifications obtained. It will be approved if it has an average greater than or equal to 9.5
If this average is higher or equal than than 16 values, then the student will be subject to an additional examination. This examination will be quoted to 4 and the final grade of the student will be 16 plus the additional examination classification.
The exam consists in a written test, quoted for 20. If the classification is or equal than than 16 values, then the student will be subject to an additional examination. This examination will be quoted to 4 and the final grade of the student will be 16 plus the additional examination classification.
The student will not be able to leave the room during the exam.
The student can not use a mobile phone. This must be turned off before the student enters the exam.
Not applicable

5. Bibliography

Recommended

Title 
Author(s) 
Matrix Analysis 
Horn and Johnson 
Matrix Theory 
Zhang 
Álgebra Linear e Geometria Analítica 
Emília Giraldes, Vitor Hugo Fernandes; Paula Smith 
Álgebra Linear com Aplicações 
Howard Anton e Chris Rorres 

Complementary

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Teacher in charge of the Curricular Unit:


Date

