Linear Algebra and Analytic Geometry I

Code:

M1010

Acronym:

M1010

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Web Page:	https://moodle2324.up.pt/course/view.php?id=2367
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:B	0	Official Study Plan	3	-	9	72	243
L:CC	0	study plan from 2021/22	2	-	9	72	243
L:F	0	Official Study Plan	2	-	9	72	243
			3
L:G	1	study plan from 2017/18	2	-	9	72	243
			3
L:M	103	Official Study Plan	1	-	9	72	243
L:MA	73	Official Study Plan	1	-	9	72	243
L:Q	1	study plan from 2016/17	3	-	9	72	243

Teaching language

Portuguese

Objectives

Understanding and ability to use the basic concepts and results related to the subjects of the syllabus.

Learning outcomes and competences

By completing this course, students should know, understand and be able to use the basic notions and results about vector spaces; Vector subspaces; subspace sums; direct sums of subspaces; linear independence; generating systems;finitely generated vector spaces; bases; dimension; linear applications; kernel and image of linear applications; inverse image of an element as translation of the kernel; characteristic of a linear transformation; linear operators; trace of a linear operator; matrices; matrix of a linear application with respect to fixed bases; change of basis; application of these concepts and results to solve systems of linear equations; Similar matrices; determinants; determinant of a linear operator; real Euclidean spaces; inner product, norm; angle between two vectors; vector product in R3; orthonormal bases; orthogonal complement; orthogonal projection.

Working method

Presencial

Program

0. Systems of linear equations; resolution and classification
1. Vector spaces; Vector subspaces; subspace sums; direct sums of subspaces; linear independence; generating systems; finitely generated vector spaces; bases; dimension.
2. Linear Applications; kernel and image of linear applications; inverse image of an element as translation of the kernel; characteristic of a linear transformation; linear operators; trace a linear operator.
3. Matrices; matrix of a linear application with respect to fixed bases; change of basis; application of these concepts and results to solve systems of linear equations; Similar matrices.
4. Determinants; determinant of a linear operator.
5. Real Euclidean spaces; inner product, norm; angle between two vectors; vector product in R3; orthonormal bases; orthogonal complement; orthogonal projection.

Mandatory literature

Gabriela Chaves; Texto de apoio, disponível na página UC do Moodle

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
Nomizu Katsumi; Fundamentals of linear algebra

Teaching methods and learning activities

Contact hours are divided into theoretical and theoretical-practical. The former consist of lectures on the contents of the syllabus, making use of examples to illustrate the concepts treated and to guide students. In the latter, theoretical and practical exercises and problems are solved. Support materials are available on the course page. In addition to the classes, there are weekly periods where students have the opportunity to ask for help on their difficulties.

Software

Wolfram Player disponível em https://www.wolfram.com/player/

keywords

Physical sciences > Mathematics > Geometry
Physical sciences > Mathematics > Algebra

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

Eligibility for exams

No condition is required to obtain frequency.

Calculation formula of final grade

Special assessment (TE, DA, ...)

Any examination requested under special statutes will consist of a written test which may be preceded by a previous oral or written test.

Observations

Any student may be required to take an oral test to clarify any doubts that may have arisen regarding the tests or assessment work.