Course teacher(s)
Thomas DEMUYNCK (Coordinator)ECTS credits
5
Language(s) of instruction
english
Course content
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)
Objectives (and/or specific learning outcomes)
At the end of this teaching unit, students are capable of applying mathematical tools to economic problems, in particular to microeconomics.
Prerequisites and Corequisites
Required and Corequired knowledge and skills
MATH-S1711: Mathematics: Calculus
MATH-S1712: Mathematics: Linear Algebra
Required and corequired courses
Teaching methods and learning activities
- Theory syllabus + exercises on UV, theoretical videos (capsules) on UV
- 12 flipped classroom sessions: Q&A + additional exercises/questions
Course notes
- Syllabus
- Université virtuelle
Other information
Contacts
Thomas DEMUYNCK Building R42 - 6e floor - office R42.6.220 - e-mail: thomas.demuynck@ulb.be
Campus
Solbosch
Evaluation
Method(s) of evaluation
- written examination
written examination
- Open question with short answer
- Open question with developed answer
- Closed question with multiple choices (MCQ)
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).
The instructor reserves the right to invite any student to an additional oral examination in order to verify their personal mastery of the content of the submitted examination, particularly where inconsistencies identified in the examination prevent the instructor from properly assessing the student’s level of mastery of the knowledge and skills targeted by the course.
Language(s) of evaluation
- english