Mathématique générale : compléments d’analyse et algèbre linéaire

This linear algebra course includes the concepts of

- real matrices (sum and product, trace, transpose, elementary matrices, invertibility of square matrices, rank of a matrix)

- linear systems (matricial form of linear systems, Cramer systems,....)

- determinants (properties, link between determinants and matrix invertibility, computation of the inverse with determinants)

- vector spaces (vector sub-spaces, linear dependence et independence, bases, change of basis, linear transformations, eigenvectors and eigenvalues, symmetric bilinear forms, scalar product, quadratic forms)

- complex numbers (sum and product, de Moivre's formula, roots of polynomials, nth roots of complex numbers)

- linear recurrence relations with constant coefficients (recurrences of order 1, recurrences of order n)

Courses requiring this course

Theory: ex-cathedra course.

Notes for the theoretical part: slides that are projected (and commented!) during the course.

Exercises: students are divided into groups for exercise sessions.

Exercise booklet divided into 12 lessons, each of which starts by a short reminder of the corresponding theory followed by some solved exercises, plus some proposed exercises (final answers (at least) are provided).
Some solved exams from previous years are available on the "université virtuelle".

During the academic year, guidance sessions and assistance are organized.

References, bibliography, and recommended reading

Cours de mathématiques pour économistes, 1989, Philippe Michel, Economica.

Mathématique pour économistes et gestionnaires, 2010, Louis Esch, 4e édition, ouvertures économiques, De Boeck Université.

Course notes

• Podcast
• Syllabus
• Université virtuelle

Contacts

Bram DE ROCK Bâtiment R42 - 6e niveau - bureau R42.6.218 - Tél.: (02) 6504214 - e-mail: Bram.De.Rock@ulb.be
Thomas DEMUYNCK Bâtiment R42 - 6e niveau - bureau R42.6.220 - Tél.: (02) 6504221 - e-mail: thomas.demuynck@ulb.be
Marjorie GASSNER Bâtiment H - 4e niveau - bureau H.4149 - Tél.: (02) 6503843 - e-mail: marjorie.gassner@ulb.be

Campus

Solbosch

Method(s) of evaluation

• written examination

written examination

A written exam on the theory as well as the exercises takes place during the May/June exam session. 

During the second exam session (August/September), a written exam of the same type as the one organized during the first exam session is organized. 

Mark calculation method (including weighting of intermediary marks)

100% written exam.

Language(s) of evaluation

• french