Linear Algebra and Analytic Geometry

Code:

M1002

Acronym:

M1002

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Computer Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	66	Plano de estudos a partir de 2014	1	-	6	56	162
L:G	4	study plan from 2017/18	3	-	6	56	162
L:Q	0	study plan from 2016/17	3	-	6	56	162
MI:ERS	97	Plano Oficial desde ano letivo 2014	1	-	6	56	162

Teaching language

Portuguese

Objectives

Upon completing this course the student should know and understand: how to solve and discuss linear systems of equations using the Gauss method with matrix notation; determinant properties for the computation of the determinant of a square matrix and knowing the cases where area and volume interpretations are given; the basic concepts and main results on vector spaces and on linear maps between finite-dimensional linear vector spaces.

Learning outcomes and competences

Upon completing this course, the student should be able to: make the main matrix operations; solve systems of linear equations using matrices; using matrices to discuss systems of linear equations; calculate determinants; apply the properties of determinants; recognize  vectorsubspaces; determine bases for real vector spaces; calculate the dimension of vector spaces; recognize linear functions, and their main properties; determine or justify why there are no linear functions satisfying certain conditions; work with matrices associated with linear functions; determine eigenvectors and eigenvalues ​​of matrices; diagonalize a matrix (if possible); using some properties of matrix diagonalization. Identify conic sections.

Working method

Presencial

Program

1. Systems of linear equations:                                           


2. Matrices     


3. Determinants:                                   


4. Vector spaces: 


5. Linear maps


6. Eigenvalues and eigenvectors


7. Conics

Mandatory literature

Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Edwards jr. C. H.; Elementary linear algebra. ISBN: 0-13-258245-7
Monteiro António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
Mansfield Larry E.; Linear algebra with geometric applications. ISBN: 0-8247-6321-1
Cabral Isabel Isabel; Álgebra linear. ISBN: 978-972-592-239-2

Teaching methods and learning activities

Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page (Moodle).

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

No requirements.

Calculation formula of final grade

Final exam. The first and second exam are divided into 3 parts.

In the first exam two groups of questions (out of 3) can be replaced by the score obtained in two tests; the first test (date: October the 24th) can replace the first group of questions and is worth 25% of the final grade (5 points); the second test (date: November the 28th) is worth 30% of the final grade (6 points) and can replace the second group of questions.

At the second examination season, the final classification of each part will always be the best between all the classifications obtained. 

Students who want to improve their grades at the second examination season will have to do the three parts on the day scheduled for the second season exam. For these students, the classifications obtained in the regular season do not count in the second examination season for the purpose of grade improvement.

In no other case will the student be allowed to replace part of the exam by a test.

Any special exam can be either an oral or a written exam. No part of these exams can be replaced by the score obtained in a test.

Examinations or Special Assignments

Any special exam can be either an oral or a written exam. No part of these exams can be replaced by the score obtained in a test.

Special assessment (TE, DA, ...)

Special exams will consist of a written test, which might be preceded by an eliminatory oral test to assess whether the student satisfies minimum requirements to tentatively pass the written test.
No part of these exams can be replaced by the score obtained in a test.

 

Classification improvement

Exam. For these students it will not be allowed to replace any part of the exam by any test.

Observations

Any student can be asked to do an oral examination in case there are some dougts about the written examination.