Linear Algebra and Analytic Geometry

Code:

M1009

Acronym:

M1009

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Web Page:	https://moodle2324.up.pt/course/view.php?id=6685
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Engineering Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:EF	71	study plan from 2021/22	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, vector space and linear map.

Learning outcomes and competences

Upon completing this course, the student should be able to: use matrix operations; solve systems of linear equations using matrices; use matrices to discuss systems of linear equations; compute determinants; apply the properties of determinants; recognise real vector subspaces; determine bases for real vector spaces; compute the dimension of vector spaces; recognise linear maps, and their main properties; determine or justify why there are no linear maps satisfying certain conditions; operate on with matrices associated with linear maps; determine eigenvectors and eigenvalues of matrices; diagonalize a matrix (if possible); use properties of matrix diagonalisation.

Working method

Presencial

Program

Sistemas lineares e matrizes
Matrizes
Determinantes de matrizes quadradas
Espaços vetoriais
Aplicações lineares
Vetores e valores próprios e diagonalização de matrizes
Cônicas
Espaço dual de um espaço vetorial

Mandatory literature

Avrizer, Dan; Geometria analítica e álgebra linear: uma visão geométrica, Editora UFMG, 2009. ISBN: 978-85-7041-754-1 (available at http://150.164.25.15/ead/acervo/livros/Geometria%20Analitica%20e%20Algebra%20Linear%20-%20Uma%20Visao%20Geometrica%20-%20TI.pdf (2 volumes))
Serge Lang; Introduction to linear algebra. ISBN: 0-387-96205-0

Complementary Bibliography

Howard Anton; Elementary linear algebra. ISBN: 0-471-03247-6
António Monteiro; Álgebra linear e geometria analítica. ISBN: 972-773-106-6
Larry E. Mansfield; 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 Moodle course webpage.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	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

N/A

Calculation formula of final grade

For approval in the tests the student should obtain a total of 9,5 points in the three tests and a mimimmum mark of 2 out of 7 in each test.

A minimum of 9.5 in the exam is required for approval.

The final mark is either the sum of the marks obtained in the tests or the result of the final exam.

Both tests and exam may be done through the Moodle course webpage.

An additional test, either written or oral, may be asked of students aiming at marks over 15 out of 20. The lower limit mark for this test will be announced after the third test.
In this case the final mark will depend only on the additional test and may take any value from the limit value to 20, independently of the results of other tests or exam.

Special assessment (TE, DA, ...)

Written exam in the same conditions as the exam in the second call.

Classification improvement

Follows the same rule as for ordinary students and takes place only at the exam in the second call.