Linear Algebra and Analytic Geometry

Code:

M1002

Acronym:

M1002

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 1S

Active?	Yes
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:B	0	Official Study Plan	3	-	6	56	162
L:CC	78	Plano de estudos a partir de 2014	1	-	6	56	162
L:G	2	study plan from 2017/18	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	6	56	162
MI:ERS	111	Plano Oficial desde ano letivo 2014	1	-	6	56	162

Teaching language

Portuguese

Objectives

Upon completing this course the student should know and understand: how to solve and discuss linear systems of equations using the Gauss method with matrix notation; determinant properties for the computation of the determinant of a square matrix and knowing the cases where area and volume interpretations are given; the basic concepts and main results on vector spaces and on linear maps between finite-dimensional linear vector spaces.

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  vectorsubspaces; 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. Systems of linear equations:                                           


2. Matrices     


3. Determinants:                                   


4. Vector spaces: 


5. Linear maps


6. Eigenvalues and eigenvectors


7. Conics

Mandatory literature

Howard Anton; Elementary linear algebra. applications version. 7th ed. ISBN: 0-471-58741-9
Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Edwards jr. C. H.; Elementary linear algebra. ISBN: 0-13-258245-7
Mansfield Larry E.; Linear algebra with geometric applications. ISBN: 0-8247-6321-1

Teaching methods and learning activities

Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page (Moodle).

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
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

No requirements.

Calculation formula of final grade

50% mid-term test + 50% final exam