Linear Algebra and Analytic Geometry

Code:

M1002

Acronym:

M1002

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=3220
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	1	Official Study Plan	3	-	6	56	162
L:CC	73	Plano de estudos a partir de 2014	1	-	6	56	162
L:G	6	study plan from 2017/18	3	-	6	56	162
L:Q	2	study plan from 2016/17	3	-	6	56	162
MI:ERS	107	Plano Oficial desde ano letivo 2014	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

Upon completing this course, the student should master the main concepts of Linear Algebra and Analytic Geometry. Namely, he must understand, be able to work with and use the main properties of the concepts of matrix, determinant, real vector space and linear function.

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 real vector subspaces; 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. Linear systems and matrices


2. Matrices


3. Determinants of square matrices


4. Real vector spaces


5. Linear functions


6. Eigenvectors and eigenvalues and diagonalization of matrices


7. Conic sections

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

Teaching methods and learning activities

Contact hours are divided into theoretical and practical classes. In the first, the contents of the course are presented using examples to illustrate them and to guide the students. In the practical classes, previously announced exercises and problems are solved. Support materials are available on the course webpage. In addition to the classes, there are periods of attendance per week where students have the opportunity to ask questions.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Calculation formula of final grade

The content of this course will be divided into two parts, each evaluated separately. The final classification will be the average of the scores obtained in each of these two parts.

Regular Season:

• The first part will be evaluated by test, which will be held on October 31st, from 18:00 to 19:30.
• The second part will be evaluated on the date set for the examination of this UC during the regular season. It should be noted that the first part of the course content will not be evaluated in the examination of this UC during the regular season.

Second examination season (except for classification improvement exams):

• The examination in the second examination season will be divided into two parts.
• At the second examination season, the final classification of each part will always be the best between the classifications obtained in the regular season and the second examination season. It should be noted that a student may choose not to do one of the parts in the second examination season, keeping the grade obtained during the regular season in that part.

Special assessment (TE, DA, ...)

Any examination required under special statutes consist of a written exam that can be preceded by an oral or written evaluation.

Classification improvement

• Students wishing to take a grade improvement examination in the regular season will have to follow the rules indicated above for the evaluation of the remaining students during the regular season.


• Students who want to improve their grades at the second examination season will have to do both parts on the day scheduled for the second season exam and the final grade will be the average of those two parts. Thus, the classifications obtained in the regular season do not count in the second examination season for the purpose of grade improvement.