2023-2024 / MATH0080-1

Differential calculus


30h Th, 30h Pr

Number of credits

 Bachelor in mathematics6 crédits 


Jean-Pierre Schneiders

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course is devoted to the differential calculus for functions of several real variables with scalar or vector values. It is the sequel of the first year analysis courses which are more focused on function of a real variable with values in R or C. Here is a summary of the table of contents:

  • R^n and its topology
  • Limits and continuity for functions of several variables
  • Uniform convergence and continuity of the limit of a sequence of continuous functions
  • Partial derivatives, directionnal derivatives, and differentials
  • Derivation of the limit of a sequence of functions and applications
  • Higher order derivatives and Taylor expansion
  • Application to the study of local extrema
  • Implicit functions theorem and consequences
  • Application to the study of conditionnal extrema

Learning outcomes of the learning unit

At the end of this course, the student should have a good knowledge of the basic tools of the differential calculus for functions of several real variables and should be able to use these tools to solve various basic problems of real analysis.
The various techniques used in the proofs should be sufficiently well mastered to be applied in other contexts.

Prerequisite knowledge and skills

Good knowledge of first year analysis and algebra.

Planned learning activities and teaching methods

The course consists of blackboard lessons and exercises sessions.
During the lessons, the main theoretical results are introduced, established and illustrated with examples.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons.
A few formative tests will be organized to allow the students to evaluate their progression.
Further informations will be provided through the eCampus page of the course.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Recommended or required readings

Lecture notes are available in PDF on the eCampus page of the course.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

Additional information:

The oral examination will deal with the theory. The written examination will deal with the exercises. The final grade will be the mean of the grades obtained during these examinations.

Work placement(s)

Organisational remarks and main changes to the course


Jean-Pierre Schneiders Département de Mathématique (Bât. B37, Bureau 1/60) Allée de la Découverte, 12 - 4000 Liège (Sart-Tilman) Tél. : (04) 366.94.01 - E-mail : jpschneiders@uliege.be Page web : http://www.analg.ulg.ac.be/jps/

Association of one or more MOOCs