Linear Algebra with Analytical Geometry I

Instance: 2013/2014 - 1S

Cycles of Study/Courses

Last updated on 2013-09-17.

Fields changed: Objectives, Resultados de aprendizagem e competências, Métodos de ensino e atividades de aprendizagem, Bibliografia Obrigatória, Melhoria de classificação, Obtenção de frequência, Componentes de Avaliação e Ocupação, Fórmula de cálculo da classificação final

Teaching language

Objectives

The student should know and understand: how to solve and discuss linear systems of equations using the Gauss method through the matrix notation; some of the more important determinant properties for the calculation of the determinant of a square matrix, using them according the particularities of the matrix, and knowing the cases where area and volume interpretations are given; the basic concepts and main results on finite-dimensional linear vector spaces, with special emphasis to the Rⁿ e Cⁿ examples, and on linear maps between finite-dimensional linear vector spaces; the euclidian space Rⁿ and some of the more important results derived from the fact that a inner product is defined on R^n;; the computation and the algebraic and geometric meaning of eigenvalue and eigenvector of a linear transformation.

Learning outcomes and competences

The student should know: how to solve and discuss linear systems of equations;how to calculate the determinant of a square matrix,using the properties of the determinant function and its area and volume interpretations; the basic concepts and main results on finite-dimensional linear vector spaces and linear maps between finite-dimensional linear vector spaces; the euclidian space Rⁿ and some of the more important results derived from the fact that  a inner product is defined on R^n;; how to compute and the algebraic and geometric meaning of eigenvalue and eigenvector of a linear transformation.

Working method

Program

Systems of linear equations and matrices (in R and C).

Determinants.

Vector spaces and linear maps (mainly in Rⁿ and Cⁿ).

The Euclidian space Rⁿ. Eigenvectors and eigenvalues.

Mandatory literature

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.

Evaluation Type

Assessment Components

Eligibility for exams

The students not attending more than 4 example classes lectures of the unit will be excluded.

The students that have been already admitted to the unit at the following previous school years, 2010/11, 2011/12 or 2012/13,  they can ask for not attending the example classes lectures. For that, they should send an e-mail till 15th of October to gchaves@fc.up.pt, indicating the name and the course.

Calculation formula of final grade

Final mark at "Época normal"

 Test 1 date: October 23 ,  9hrs30m-11hrs.

Test 1 classification: Y (out of 7).

 Test 2 date: December 18, 9hrs-11hrs30m.

Test 2 classification: Z (out of 13).

Final mark at "época normal":

(Y + Z)  if (Y + Z) is greater or equal to 10 and the student didn't make the exam at "época normal".

Exam classification: X (out of 20);

Final mark at "época normal":

X if the student made the "época normal" exam.

Remark 1: The "época normal" exam will consist of two parts, the first one marking out of 7 and the second one marking out of 13, in correspondence to the material that have been evaluated at test 1 and 2. 

The student can decide not to make one of the parts of the exam, and then it will be considered the classification obtained by the student at the corresponding test. 

Final mark at Época de recurso

Final mark: mark obtained at the exam of "Época de recurso" (out of 20).

Remark 2: The "época de recurso" exam will consist of two parts, the first one marking out of 7 and the second one marking out of 13, in correspondence to the material that have been evaluated at test 1 and 2. The student that was not approved at "Época normal" can decide not to make one of the parts of the exam, and then it will be considered the classification obtained by the student at the corresponding test.

Remark 3: The student that was approved at "Época normal"  can't use the classification(s) obtained by him at the test(s) if he decides to make the exam of "Época de recurso" for improving his final mark at the course.
 

Remark 4: At the "Época de recurso" exam, it is not possible to use the classification obtained  at any of the two parts of the"Época normal" exam. 

Final marks above 16

The students that have marks above 16 (at the two tests, or at the "Época normal" exam, or at the"Época de recurso" exam) will have to do an additional written test, at date after the "Época normal" exam.

Special assessment (TE, DA, ...)

Any student asking for an exam because of special conditions of his registration will do a written exam, but possibly, only, after an extra written or oral examination, in order to check if the student has a minimum knowledge about the unit so that he can do the special exam.

Classification improvement

The student that was approved at "Época normal"  can't use the classification(s) obtained by him at the test(s) if he decides to make the exam of "Época de recurso" for improving his final mark at the course. 

The student that has been approved at the school year 2012/13 and decides to improve his final mark at the course, he can do that only by making the exam and not by doing the tests.

Observations

Unit jury: Maria Gabriela Faria Arala Chaves; Ana Paula da Silva Dias.