Linear Algebra and Analytic Geometry II

Code:

M1036

Acronym:

M1036

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 2S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	87	Official Study Plan	1	-	9	72	243
L:MA	60	Official Study Plan	1	-	9	72	243

Teaching language

Portuguese

Objectives

To introduce the basic concepts and results associated to matrices diagonalization and its application to geometry.

Learning outcomes and competences

A student is expected to know the concepts and basic results introduced  and to master the associated techniques.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

It is assumed in this course that the student is familiar and is capable of using the basic notions of Linear Algebra given in the previous course Álgebra Linear e Geometria Analítica I.

Program

. Eigenvectors and eigenvalues, diagonalizable matrices.
. Self-adjoint endomorphisms.
. Linear isometries and orthogonal matrices.
. Symmetrical bilinear forms and quadratic forms.

Mandatory literature

Texto de apoio; disponível na página da disciplina no Moodle.

Complementary Bibliography

António Monteiro; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
C. H. Edwards, Jr; Elementary linear algebra. ISBN: 0-13-258245-7
Howard Anton; Elementary linear algebra. ISBN: 0-471-66959-8
Larry E. Mansfield; Linear algebra with geometric applications. ISBN: 0-8247-6321-1
Luís T. Magalhães; Algebra linear como introducao a matematica aplicada. 5ª ed. ISBN: 972-47-007-0

Teaching methods and learning activities

The content of the syllabus is presented at the lectures, and proposed exercises are solved by the students at the practical classes.

Software

Wolfram|Alpha: Computational Intelligence

keywords

Physical sciences > Mathematics > Mathematical logic
Physical sciences > Mathematics > Algebra > Set theory
Physical sciences > Mathematics > Number theory

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	171,00
Frequência das aulas	72,00
Total:	243,00

Eligibility for exams

No requirements.

Calculation formula of final grade

- Approval to the course is obtained by taking the final exam.

- Any final exam consists of 2 parts, each graded to 10 (out of 20).

- At the second or special exam season, students who have not yet obtained approval (and only these) may choose not to solve one part of the exam, that would then get the grade of the corresponding part of the exam in the first exam season.

- The possibility mentioned in the previous paragraph does not apply to the exam to improve the classification.

- In any situation, each part solved in a final exam will be assigned the classification of that resolution.

Special assessment (TE, DA, ...)

In any special evaluation season, the written exam might be preceded by an eliminatory oral test to assess whether the student satisfies minimum requirements to tentatively pass the written exam.

Classification improvement

Students wishing to undertake a classification improvement must solve all parts of the exam.

Observations

It may be asked to any student to take an extra oral or written examination if any doubt concerning his/her performance occurs on certain assessment pieces.