Linear Algebra and Analytic Geometry

Code:

M1002

Acronym:

M1002

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 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:CC	69	Plano de estudos a partir de 2014	1	-	6	56	162
MI:ERS	127	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 (%)
Teste	100,00
Total:	100,00

Calculation formula of final grade

The content of this course will be divided into three parts, each evaluated by a test. The final grade is the everage of the three parts, but it is required to have a test score higher than 4 points in the 3rd part to get approval to this course. The dates for the completion of the three tests are:

• 1st test: October 27th, 17:30 to 18:30
• 2nd test: November 26th, from 17:30 to 18:30
• 3rd test: the examination date scheduled for the 1st examination season

1st evaluation season:

• The final grade of the 1st evaluation season is the average of 3 tests.

2nd evaluation season:

• In the 2nd evaluation season exam, the students can repeat again all three tests or only some of them.
• The grade of each part is calculated as follows:
  • it is the grade obtained in the 1st evaluation season if the student does not do the corresponding test in the 2nd evaluation season;
  • it is the grade obtained in the 2nd evaluation season test if this grade is higher than the grade obtained in the corresponding test of the 1st evaluation season.
  • it is the average of the grades obtained in the corresponding tests if the grade obtained in the test form the 2nd evaluation season exam is less than the grade obtained in the test form the 1st evaluation season.
• The final grade of the 2nd evaluation season is the average of the grades of the three parts obtained as explained above.

Special assessment (TE, DA, ...)

Any examination required under special statutes consist of a written exam that can be preceded by an assessment (oral or written) to evaluate if the student is in minimum conditions of trying to get approval to discipline in the written exam.

Classification improvement

• Students who wish to take a classification improvement exam in the 1st examination season will have to do all three tests and the final grade is the average of the scores of the 3 tests.


• Students who want to improve their grades in the 2nd examination season have to do all 3 tests in the 2nd examination season exam date and the final grade is the average of the scores obtained in these 3 tests.