Linear Algebra and Analytical Geometry

Code:

L.EIC001

Acronym:

ALGA

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Web Page:	https://moodle2425.up.pt/course/view.php?id=4115
Responsible unit:	Department of Informatics Engineering
Course/CS Responsible:	Bachelor in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EIC	320	Syllabus	1	-	4,5	39	121,5

Teaching language

Suitable for English-speaking students

Objectives

This course has two main objectives: the promotion of logical reasoning and methods of analysis and the introduction and theoretical development of a set of concepts that will be fundamental to support the study of other disciplines along this course of studies.

Learning outcomes and competences

The course aims developing mathematical tools used in Engineering.

The student should master the main concepts of vector algebra in R^n, with special emphasis on R^2 and R^3. Students must be able to use the main properties of the concepts of matrix, determinant, vector space and linear map.

In particular, the student should be able to:

- recognize real vector spaces and subspaces, determine their bases, compute their dimension and coordinates of vectors on a basis;

- recognize linear maps, and their main properties;

- work with matrix operations and use them to solve systems of linear equations and to discuss them, operate with matrices associated with linear maps; determine eigenvectors and eigenvalues, diagonalize a matrix (if possible), and if time permits, identify conics and quadrics using matrices and eigenvalues;

- compute determinants, apply their properties and their geometric interpretation as area and volume.

Working method

Presencial

Program

Matrices: matrix operations; determinant of a square matrix.

Systems of real linear equations and matrices: Gauss Method; Cramer Rule.

The Euclidian space R^n: linear independence, basis, dimension, coordinates. Cross product and scalar triplet product. Applications to systems of real linear equations, lines and planes. Geometric interpretation of 2x2 and 3x3 matrices determinant.

Linear maps in R^n. Basis and change of bases matrices.

Eigenvectors and eigenvalues of a linear endomorphism and of a matrix; diagonalizable linear endomorphism and matrix; symmetric matrices.

(Optional, if time permits) Spectral Theorem for symmetric matrices and its application to identify conics and quadrics.

Mandatory literature

Anton, Howard; Elementary linear algebra. ISBN: 0-471-44902-4
Luís T. Magalhães; Álgebra linear como introdução a matemática aplicada. ISBN: 972-47-0007-0
Monteiro, António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8

Teaching methods and learning activities

Lectures and example classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, giving the solution to previously indicated exercises and problems. All resources are available for students at the unit’s web page. The lecturer(s) have weekly office hours for discussion of difficulties with students.

Evaluation: continuous evaluation without final exam. The continuous evaluation will include two written tests.

Software

WolframAlpha https://www.wolframalpha.com/

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	82,50
Frequência das aulas	39,00
Total:	121,50

Eligibility for exams

No condition is required to obtain frequency.

Calculation formula of final grade

(iv) The final grade will be the sum of the obtained scores.

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

Students aiming to improve their grade must take both parts of the resit exam.

Observations