Face-to-face , second term, 45 hours of theory and 22,5 hours of exercises.

Second term
Monday from 08:00 to 08:45 at 43 Botanique 1
Tuesday from 14:00 to 16:00 at 43 Botanique 1
Thursday from 11:00 to 13:00 at 43 Botanique 1

French

As far as the content is concerned, by the end of the course the student should have completed his knowledge of the real functions of a real variable (integrals) and familiarised himself with the theory of functions of two or more variables.
For each studied subject, the student should be able to define and explain the concepts, justify the successive stages of a demonstration, implement the calculation techniques and solve simple problems.
This course also aims to enable the students to use mathematical concepts in economic contexts.

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The studied themes are:
- the Riemann integral and its many applications (calculation of areas, volumes and arc length of curve);
- the functions of several variables (partial derivative, differential, directional derivative, extreme values, Lagrangian, double integrals).

The titles of the chapters give an idea of the notions that will be studied in the course:
Chapter 5: Integrals
Chapter 6: Application of integrals
Chapter 9: Vectors and the geometry of space
Chapter 10: Vector functions
Chapter 11: Partial derivatives
Chapter 12: Multiple integrals

The subject matter is subdivided into 11 modules, precisely defined by the sections of the book.

At the beginning of each week, the students are asked to work on one module by themselves - both from the theoretical point of view and from the point of view of basic exercises. This familiarisation involves, among other things, that they repeat on their own the proposed exercises, that they review and understand the various theoretical elements involved in the module, that they complete some short exercises (often at the start of the exercises suggested at the end of the section), that they get used to the notations and follow the course, which resumes and deepens elements of the module.

During the weekly lecture given to all the students, the professor focuses on the essential points of the module, adds some supplementary information or deepens certain theoretical points.

Each week, the student will take a short test designed to assess an initial understanding. The corrected tests are handed back to students during the tutorials (Monday 8:00 to 9:00, room 1). These tests are mandatory and will be taken into account for the final mark (see below).

Course extension

For the INGE students, the course will continue on the basis of 3 hours per week (without tests) in order to develop the subject matter specific to their orientation.

Exercise sessions (tutorials)

Students are divided into groups. It is imperative to respect this distribution as the size and stability of the groups has a direct impact on the quality of individual and collective work that is requested during these weekly two-hour sessions.

The sessions are organised in three stages and based on the preparations of students. Specifically, a selection of exercises will be posted on the course website (on eSaintLouis) minimum one week before each tutorial. It is up to the students to prepare these exercises before the session. The tutorial session takes place according to the following structure:

- A short introduction in which students revise, through basic exercises the fundamental elements and techniques. During this part and on the basis of their preparation, students work alone. Probationary lecturers answered questions.
- The second, longer part, sees students work in interaction with the probationary lecturer on exercises using the fundamental elements and techniques, and/or implementing less immediate reflections and/or referring to and implementing theoretical developments.
- During the last part, exercises from previous exams are proposed. Students work alone. Probationary lecturers answered questions.

A syllabus of exercises is available at the reprography service.

It is obvious that all the exercises in this syllabus will not be solved during the tutorials. Although the exercises completed during the tutorials represent a diverse range of exercises, it is strongly recommended that students try to solve the other exercises (even the other exercises included in the reference books).

Instructorship

Accompanying instructorships are organised (for practical information: see information boards).
Note: Remedial tutoring for the General Mathematics course is organised alternately with the infinitesimal Mathematics tutoring (for practical information: see information boards).

The final evaluation takes into account two marks: the mark of the continuous evaluation, and the mark of the final examination.
(This rule is strict for the June session and to the advantage of the student for the possible August-September session).

Continuous evaluation: The 6 best weekly tests out of 11 will be selected and will count for 6 points out of 20 of the final mark.
Important remark: the tests are designed to assess an initial understanding; the questions that are asked are fundamental. On no account can they be considered as examples of future examination questions: the final examination supposes indeed an further deepening of the subject matter, which cannot be asked after an initial learning.

Final examination: Written examination. Calculators are forbidden. The students have at their disposal the form from the book. The final examination will count for 14 points out of 20 of the final mark. It includes different types of questions:
- short questions designed to verify the acquisition of the techniques
- questions aimed at verifying the acquisition of the theory, the understanding of concepts, the mastery of the technical language;
- questions that require development, that assess the synthesis, writing and structuring abilities, but also the depth of the understanding, the ability to argue and the know-how when faced with a new mathematical problem.

Written supports of the course:
- Analyse, Concepts et contextes, Volume 1, Fonctions d'une variable, de STEWART J., De Boeck Université 2001.
- Analyse, Concepts et contextes, Volume 2, Fonctions de plusieurs variables, de STEWART J., De Boeck Université 2001.

Syllabus of Infinitesimal Mathematics available at the reprography service.