Duration
30h Th, 30h Pr
Number of credits
| Bachelor in mathematics | 6 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
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 his 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
- 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
- Derivation of the limit of a sequence of functions and applications
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.
Organisational adjustments related to the current health context
The space in the classroom being sufficient, the course will be face-to face under yellow or orange code. The exams will also be face-to-face in the same situation.
Recommended or required readings
Lecture notes will be available in PDF on the eCampus page of the course.
Assessment methods and criteria
Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.
An examination comprising an oral part on the theory and a written part on the exercices will be organized during the first session.
A similar examination will be organized during the second session.
Work placement(s)
Organizational remarks
Contacts
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/