Linear Algebra and Analytic Geometry

Code:

M1038

Acronym:

M1038

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
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:EF	79	study plan from 2021/22	1	-	6	48	162
L:F	51	Official Study Plan	1	-	6	48	162
			3

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


8. Dual space.

Mandatory literature

Ana Paula Santana; Introdução à álgebra linear. ISBN: 978-989-616-372-3
Isabel Cabral; Álgebra linear. ISBN: 978-972-592-239-2
Howard Anton, Chris Rorres; Elementary Linear Algebra - Applications Version, 9 edition. ISBN: ISBN 13: 978-0471669593

Complementary Bibliography

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
Howard Anton, Chris Rorres; STUDENT SOLUTIONS MANUAL TO ACCOMPANY Elementary Linear Algebra with Applications 9 edition, Wiley, 2005. ISBN: ISBN-13 978- 0-471-43329-3

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 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	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

No requirements.

Calculation formula of final grade

Examinations or Special Assignments

Written or oral exam.

Special assessment (TE, DA, ...)

Written or oral exam.

Classification improvement

Exam. These students will not be allowed to take part of the continuous assessment of the course.

Observations

Artigo 13º do Regulamento Geral para Avaliação dos Discentes de Primeiros Ciclos, de Ciclos de Estudos Integrados de Mestrado e de Segundos Ciclos da U.Porto, aprovado em 19 de Maio de 2010 (cf. http://www.fc.up.pt/fcup/documentos/documentos.php?ap=3&ano=2011): "A fraude cometida na realização de uma prova, em qualquer das suas modalidades, implica a anulação da mesma e a comunicação ao órgão estatutariamente competente para eventual processo disciplinar."

Any student may be required to take an oral examination should there be any doubts concerning his/her performance on certain assessment pieces.