Linear Algebra and Analytic Geometry

Code:

M1004

Acronym:

M1004

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=405
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Physics

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	0	study plan from 2021/22	2	-	6	56	162
L:EF	76	study plan from 2021/22	1	-	6	56	162
L:F	0	Official Study Plan	3	-	6	56	162
L:G	1	study plan from 2017/18	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	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; recognize real vector subspaces; determine bases for real vector spaces; compute the dimension of vector spaces; recognize 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 diagonalization.

Working method

Presencial

Program

1. Linear systems and matrices


2. Matrices


3. Determinants of square matrices


4. Vector spaces


5. Linear maps


6. Eigenvectors and eigenvalues and diagonalization of matrices


7. Conic sections


8. Dual of a vector space

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))

Complementary Bibliography

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

Comments from the literature

the textbook, in portuguese, is available at:
Vol 1
http://150.164.25.15/ead/acervo/livros/Geometria%20Analitica%20e%20Algebra%20Linear%20-%20Uma%20Visao%20Geometrica%20-%20TI.pdf
Vol 2
http://www.mat.ufmg.br/ead/wp-content/uploads/2016/08/Geometria-Analitica-e-Algebra-Linear-Uma-Visao-Geometrica-TII.pdf

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.

In the classroom version,  theoretical and practical classes are direct contact between lecturer and students. In addition to the classes, there are designated times every week where students have the opportunity to ask questions.

In distance learning,  classes are replaced either by online presentations or by online texts with exposition of theory and discussion of examples available on the Moodle course webpage as well as proposed problems to be solved, with solutions provided some days later. There will also be online forums for discussion of difficulties  on the Moodle course webpage.

The choice between classroom version and distance learning will be announced at the start of term and depends on the epidemiological situation. There may be a switch in version at any moment, if need arises.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	90,00
Prova oral	10,00
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 mimimum 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 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, ...)

Any examination required under special statutes consist of a written exam (either in classroom or via Moodle) that may be preceded by an oral or written evaluation.

Classification improvement

Folows the same rule as for ordinary students and takes place only at the final exam.