Linear Algebra and Analytic Geometry
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2020/2021 - 1S
Cycles of Study/Courses
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
- Systems of linear equations:
- Matrices
- Determinants:
- Vector spaces:
- Linear maps
- Eigenvalues and eigenvectors
- 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
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.