année académique
2025-2026
2026-2027

Titulaire(s) du cours

Thomas DEMUYNCK (Coordonnateur)

Crédits ECTS

5

Langue(s) d'enseignement

anglais

Contenu du cours

Functions of Several Real Variables, More Specifically:

  • Differential equations
  • Cartesian products, functions, domain of definition, vertical sections, norm, Euclidean distance, dot product, closed and open balls
  • Properties and topology of ℝⁿ (convergent sequences, open sets, closed sets, bounded sets, compact sets, convex sets, interior points, adherent points, and accumulation points)
  • Limits and continuity (properties of limits)
  • Partial derivatives (partial differentiability, elasticities, gradient vector, Schwarz's theorem, Hessian matrix)
  • Tangent plane, differential, functions from ℝⁿ to ℝᵐ (limits, Jacobian matrix, function composition, differentiation of composed functions)
  • Homogeneous functions (homogeneity of partial derivatives, Euler’s theorem), directional derivatives, Taylor’s formula
  • Convex (and concave) sets and functions
  • Implicit function theorems
  • Unconstrained optimization (necessary and sufficient conditions)
  • Optimization with equality constraints (Lagrange’s theorem)
  • Optimization with inequality constraints (Kuhn-Tucker theorem)

Objectifs (et/ou acquis d'apprentissages spécifiques)

At the end of this teaching unit, students are capable of applying mathematical tools to economic problems, in particular to microeconomics.

Pré-requis et Co-requis

Connaissances et compétences pré-requises ou co-requises

MATH-S1711: Mathematics: Calculus
MATH-S1712: Mathematics: Linear Algebra

Méthodes d'enseignement et activités d'apprentissages

  • Theory sullabus + exercises on UV, theoretical videos (capsules) on UV
  • 12 flipped classroom sessions: Q&A + additional exercises/questions
  • 12 practical sessions (TP): students are divided into groups. The exercises are in the syllabus (with final answers and ome detailed solutions)
     

Références, bibliographie et lectures recommandées

Thomas DEMUYNCK Building R42 - 6e floor - office R42.6.220 - e-mail: thomas.demuynck@ulb.be

Support(s) de cours

  • Université virtuelle
  • Syllabus

Autres renseignements

Campus

Solbosch

Evaluation

Méthode(s) d'évaluation

  • Examen écrit

Examen écrit

  • Question ouverte à réponse courte
  • Question ouverte à développement long
  • Question fermée à Choix Multiple (QCM)

A written exam covering theory and exercises will be organized during the January session. The second session is of the same type as the first session. Some questions may be multiple choice (MCQ).
A

Langue(s) d'évaluation

  • partiellement en anglais

Programmes