Course description

Title of the Teaching Unit

Advanced Mathematics 2

Code of the Teaching Unit

12UMQ20

Academic year

2023 - 2024

Cycle

Number of credits

Number of hours

Quarter

Weighting

Site

Anjou

Teaching language

French

Teacher in charge

ENGELBEEN Céline

Objectives and contribution to the program

To create in the student a sufficiently broad mathematical culture to enable him/her to approach serenely the quantitative problems that he/she is likely to encounter in his/her professional life. At the end of the undergraduate courses in analysis, the student should be able to :
- to apprehend the numerous management disciplines that call upon mathematical tools, including in the field of production management and in the technical field,
- to assimilate new quantitative techniques that he may be required to use during his career,
- to realize that a problem encountered is likely to receive a solution that uses mathematical tools, and to integrate, if necessary, into an internal or external team responsible for solving the problem,
- to grasp the meaning and scope of the very numerous publications in the field of management that make use of mathematical tools, to make a critical judgment on these publications and, where appropriate, to transpose or contribute to transposing the proposed solutions within the framework of the organization of which he or she is a member,
- to pursue, where appropriate, complementary studies or engage in research activities, including in areas of management where mathematical tools play an important role.

More generally, mathematics constitutes a formal language whose knowledge imposes and promotes the structuring of reasoning, from the level of elementary logic to techniques for reasoning in the uncertain. In addition to the aspects of know-how mentioned above, the course must thus contribute to the development of the student's knowledge:
- the sense of rigor through the precision required by any mathematical formulation of a problem as well as the search for its solution,
- the creativity required to translate a problem initially posed in general terms into mathematical terms.
The student must be able to precisely define all the concepts introduced. He/she must be able to explain the meaning, scope and usefulness of these concepts and illustrate them with examples.
The student must be able to explain and justify the methods of calculation introduced.

When reading the statement of a problem to be solved, the student must be able to situate the problem in the whole subject, to choose the method to be used to solve it, to verify that the hypotheses required for the use of the method are well verified and finally to use the method correctly.
More generally, the student must acquire the ability to model a situation, i.e. to select from the mass of available information those that are useful and to translate them into mathematical language.
Finally, the student must be able to translate clearly and correctly into French the results obtained at the end of a problem.

Prerequisites and corequisites

The following "UE" are corequisite:
- Advanced Mathematics 1
- Advanced Mathematics and Statistics 1

Content

A. Introduction (Taylor series, complex numbers)
B. Optimization of the functions of one variable
C. Functions of several variables
D. Optimization of the functions of several variables
E. Optimization of the functions of several variables under constraints of equality
F. Optimization algorithms

Teaching methods

Type of teaching: ex cathedra plus exercise sessions.
The course alternates theoretical presentations and exercises designed to facilitate the assimilation of the notions introduced.
A series of exercises is proposed after each chapter. The home resolution of these exercises plays an important role in the assimilation of the subject matter; they allow the student to evaluate his or her degree of mastery of the subject matter taught and are the privileged instrument of preparation for the exam.
More generally, it should be emphasized that the working method must be based on reflection: memorization is not enough. It is essential not to allow any misunderstanding to pass: any statement must be able to be explained or justified. The student will only be able to achieve such a result through regular and in-depth work, which will take time but will allow him/her to acquire a structured mind.
From a practical point of view, the theoretical course will be given at a distance by video capsules. The practical sessions will be given face-to-face, but not all students will have access to them at the same time. Indeed, in order to respect the sanitary rules, all students will be divided into several groups, and the groups will alternate from week to week to the exercise sessions. This is why all the resolutions proposed during the face-to-face session will also be available in videos or files on the course website.

Assessment method

The exam is oral and closed book. It consists of theory questions and exercises of the same level as those done during the quadrimester. Accuracy and comprehension are the essential criteria for scoring.

References

• Frank Ayres Jr., Matrices - Cours et problèmes, série Schaum, McGraw Hill, 1973
• Frank Ayres Jr., Théorie et applications du calcul différentiel et intégral, série Schaum. McGraw Hill, 1972
• P. Balestra, Calcul matriciel pour économistes, éd. Castella, Albeuve (Suisse), 1972
• Alpha C. Chiang, Fundamental methods of mathematical economics, 3ème édition, Mc Graw Hill, 1984
• T.M. Flett, Mathematical analysis, McGraw Hill, 1966.
• Ernest F. Haeussler Jr., Richard S. Paul, Introductory Mathematical Analysis for Business Economics and the life and Social sciences, Prentice-Hall, 1987
• David C. Lay, Algèbre linéaire – théorie, exercices et applications, traduction de la troisième édition américaine par Micheline Citta-Vanthemsche, De Boeck et Larcier, 2004
• Stewart J., Analyse, Concepts et contextes, Volume 1, Fonctions d’une Variable, Traduction de la 1ère édition par Micheline Citta, De Boeck Université, Bruxelles, 2001
• Stewart J., Analyse, Concepts et contextes, Volume 2, Fonctions de plusieurs Variables, Traduction de la 1ère édition par Micheline Citta, De Boeck Université, Bruxelles, 2001
• Swokowski, Analyse, Traduit de l’anglais par Micheline Citta, De Boeck Université, De Boeck – Wesmael, Bruxelles, 1993
• Knut Sydsaeter, Peter Hammond, Essential Mathematics for economic analysis, Pearson Education, second edition, 2006.