Mathématique : fonctions de plusieurs variables

Functions of several real variables, more precisely:

- properties and topology of IR^n (open and closed balls, convergent sequences, open and closed sets; interior, adherent and accumulation points).

- limits and continuity (properties of limits, continuous image of a compact set).

- partial derivatives (partial differentiability, gradient, Schwarz's theorem).

- differentiability (definition, properties of differentiable functions, sufficient condition for differentiability).

- functions mapping IR^n into IR^m (limits, jacobian matrix, differentiability, composition of functions, the chain rule).

- homogenous functions (homogeneity of partial derivatives, Euler's theorem).

- directional derivatives.

- Taylor expansions.

- convex sets and convex functions.

- implicit function theorems.

- optimization (unconstrained optimization, optimization subject to nonnegativity constraints, to equality constraints (theorem of Lagrange, sufficient conditions, interpretation of Lagrange multipliers), to inequality contraints (theorem of Kuhn and Tucker)).

At the end of the course, students will be abble to apply the mathematical tools which are indispensable for several courses in economics and econometrics.

Required and corequired courses

Theory: ex-cathedra course.

Notes for the theoretical part: slides which 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, assistance is provided.

Contribution to the teaching profile

LG2. Academic mindset
LO 2.2  Display critical thinking, logical and abstract reasoning and develop an independent approach to learning

LG3. Quantitative skills
LO 3.1  Solve standard mathematical problems
LO 3.3  Assess the quality of the a quantitative analysis of an economic problem

References, bibliography, and recommended reading

Cours de mathématiques pour économistes, 1989, Philippe Michel, Economica
Mathématiques pour économistes, 1998, Carl P. Simon et Lawrence Blume, ouvertures économiques, De Boeck université
Fundamental Methods of Mathematical Economics, 2005, A.C. Chiang, K. Wainwright, McGraw-Hill Education.

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

• Other

Other

A written exam on the theory as well as the exercises takes place during the January 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)

The exam is graded out of 20.

Language(s) of evaluation

• french