Algebra

Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).

5 credits

30.0 h + 30.0 h

Teacher(s)

Glineur François; Jungers Raphaël; Remacle Jean-François; SOMEBODY; Wertz Vincent (coordinator);

Language

French

Main themes

Linear algebra : linear equation systems, matrix calculus, linear applications, euclidean spaces, vector spaces on a field, linear sequences, quadratic forms. Modelling and solving of simple problems.

Aims

At the end of this learning unit, the student is able to :

Contribution of the course to the program objectives
Regarding the learning outcomes of the program of Bachelor in Engineering, this course contributes to the development and the acquisition of the following learning outcomes:

LO1.1, 1.2
LO 2.2, 2.3, 2.4, 2.6, 2.7
LO 3.1, 3.2, 3.3
LO 4.1, 4.4

Specific learning outcomes of the course
At the end of the course the students will be able to

Master the elementary notions of linear algebra ;
Apply the notion of euclidean space and orthogonal projection to solve approximation problems in Rn and other spaces;
Calculate vector spaces of a linear operator;
Diagonalize a linear space if possible;
Study the evoluation of a linear system and of a linear recurrence:
Determine the caracteristics of a quadratic form;
Understand the main mathematical proof techniques ;
Make a critical reading and analysis of a problem statement;
Find examples and counter-examples related to a mathematical statement;
Write short mathematical proofs with rigor;
Modelli of simple problems, and problem solving using the methods cited above.

Content

Systems of linear equations,
Matrix calculus,
Vector spaces,
Linear applications,
Euclidean spaces, orthogonal projection and approximation problems,
Linear operators, eigenvectors and diagonalization, Jordan form and matrix exponential
Adjoint operator, spectral theorem, quadratic forms, law of inertia,
Sequences and series, linear differential equations

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Lectures in auditorium, supervised exercise sessions and problem based learning, possibly supplemented with writing assignments and online exercises.
Some of the above activities (lectures, exercise sessions, problem based learning) may be organised on line.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Students will be evaluated with an individual written exam, based on the above-mentioned objectives. Results from continuous assessment may also be taken into account for the final grade. The exact modalities will be specified in class.
In case of doubt after the written exam, some students may be invited to pass an oral exam.
The students presenting only a part of the course (partims A and B) may undergo an oral exam instead of a written one.

Online resources

https://moodleucl.uclouvain.be/course/view.php?id=12098

Bibliography

G. Strang, Introduction to linear algebra, 5th edition

G. Strang, Introduction to linear algebra, 5th edition, Cambridge University Press

Teaching materials

G. Strang, Introduction to linear algebra, 5th edition

Faculty or entity

BTCI

Force majeure

Evaluation methods

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme

Sigle

Credits

Prerequisites

Aims

Bachelor in Engineering : Architecture

ARCH1BA

Bachelor in Engineering

FSA1BA