Linear Algebra and Analytic Geometry
| Code: | M1002 | Acronym: | M1002 | Level: | 100 |
| Keywords | |
|---|---|
| Classification | Keyword |
| OFICIAL | Mathematics |
Instance: 2022/2023 - 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:CC | 88 | study plan from 2021/22 | 1 | - | 6 | 56 | 162 |
| L:IACD | 81 | study plan from 2021/22 | 1 | - | 6 | 56 | 162 |
Teaching language
PortugueseObjectives
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
PresencialProgram
- Systems of linear equations:
- Matrices
- Determinants:
- Vector spaces:
- Linear maps
- Eigenvalues and eigenvectors
- Conics
Mandatory literature
Ana Paula Santana; Introdução à álgebra linear. ISBN: 978-989-616-372-3Isabel 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: 0-13-258245-7Mansfield 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 examAssessment Components
| designation | Weight (%) |
|---|---|
| Teste | 100,00 |
| 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
Assessment in "época normal" will be based on two face-to-face tests, worth 8 and 12 points and on 4 quizzes.
The first test will take 75 minutes and the last 105 minutes. The first test will be on a day indicated at the begining of classes and the second on the day of "exame da época normal".
The 4 quizzes are together worth 1 point (so 0.25 each) and are done on computer using Moodle. The dates for the quizzes will be set at the beginning of the term.
If T1 is the score of the first test, T2 the score of the second, Q the sum of the scores obtained in the 4 quizzes, a student will pass the course if
T1+T2+Q ≥ 9.5
and the final mark is
min{ T1+T2+Q , 20 }.
If for for some reason it won't be possible to do face to face writen tests during the semester, the two tests will be done on the day of the exam (also face to face).
Make-up exam:
Students who still need to pass: exam with two parts, each part corresponding to one of the tests:
- The student may choose to take any parts of the exam or use classifications of corresponding parts obtained in tests.
- If they choose to do a part of the exam, it will be the classification obtained there for the final grade.
- the final grade is computed as above.
Students trying to improve their grade will have to write the whole exam (face to face) and they will not be allowed to use testes or quizzes.
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.
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