Linear Algebra with Analytical Geometry I

Code:

M143

Acronym:

M143

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=757
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:AST	0	Plano de Estudos a partir de 2008	1	-	7,5	-	202,5
L:F	53	Plano de estudos a partir de 2008	1	-	7,5	-	202,5
MI:EF	42	Plano de Estudos a partir de 2007	1	-	7,5	-	202,5

Teaching language

Portuguese

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 vector spaces 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

Presencial

Program

• Systems of linear equations.


• Matrices.


• Determinants.


• Vector spaces.


• Linear maps.


• Eigenvalues and eigenvectors.


• Euclidian space Rⁿ. Eigenvectors and eigenvalues.

Mandatory literature

Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Edwards jr. C. H.; Elementary linear algebra. ISBN: 0-13-258245-7
Monteiro António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
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.

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Eligibility for exams

No requirements.

Calculation formula of final grade

Final exam (for the first and second exam and for students that are not trying to improve their final grade), where one group of questions (out of 2) can be replaced by the score obtained in one test, worth 10/20, about the first half of the syllabus.

In no other case will the student be allowed to replace part of the exam by a test.

Any special exam can be either an oral or a written exam. No part of these exams can be replaced by the score obtained in a test.

Examinations or Special Assignments

Any special exam can be either an oral or a written exam. No part of these exams can be replaced by the score obtained in a test.

Special assessment (TE, DA, ...)

Special exams will consist of a written test, which might be preceded by an eliminatory oral test to assess whether the student satisfies minimum requirements to tentatively pass the written test.
No part of these exams can be replaced by the score obtained in a test.

 

Classification improvement

Exam. For these students it will not be allowed to replace any part of the exam by any test.

Observations

Any student can be asked to do an oral examination in case there are some dougts about the written examination.