 | |
| MATH0202-1 | Analysis I
- Part a) Introduction to the analysis academic study
- Part b) Analysis
 |
|
| Duration : | Part a) Introduction to the analysis academic study : 15h Th
Part b) Analysis : 85h Th, 60h Pr
|
|
| Credits/ECTS : |
|
|
| Holder(s) : | Part a) Introduction to the analysis academic study : Samuel Nicolay
Part b) Analysis : Samuel Nicolay
|
|
| Language : | French language |
|
| Course contents : |
 | | Part a) Introduction to the analysis academic study |
|
| As an introduction, we present the naive set theory. We also define the d-dimensional Euclidian space and give the basic properties related to these spaces. One of the aim of this course is to practise the mathematical reasonig. |
| | Part b) Analysis |
|
| Mathematical analysis is the branch of mathematics concerned with the notion of limit.
We will present in this course the concept of limit of a sequence in the Euclidean space. We will then consider the functions and their properties (continuity, derivation,...). We will also introduce some elementary functions (exponential function, trigonometric functions,...). The primitivation and the differential equations will be also presented. The end of the course is devoted to an introduction to the integral calculus. |
|
|
| Course objective : |
| | Part b) Analysis |
|
| The aim of this course is to introduce the basic notions and results concerning the mathematical analysis in the Euclidian spaces. |
|
|
| Prerequisites : |
| | Part b) Analysis |
|
| There is no pre-necessary. Of course, abilities to mathematical reasoning are an asset. One of the aims of the beginning of this course is to train these capabilities. |
|
|
| Workshops : |
| | Part b) Analysis |
|
| The exercices, directed by the assistants, are mainly dedicated to the resolution of exercises related to the theory taught during the course. They are also useful to obtain supplementary informations and to illustrate concepts tackled during the theoretical course. |
|
|
| Organization : |
| | Part b) Analysis |
|
| The timetable will be available at the beginning of the academic year. Concerning the exercises, a detailed schedule as well as informations about how the students will be split into groups will be also distributed. |
|
|
| Written notes : |
| | Part b) Analysis |
|
| Course notes (in french), following the main taught subjects, are available at the beginning of the year. |
|
|
| Assessment : |
| | Part b) Analysis |
|
| Students are tested all along the year. These tests are aimed to encourage regular work and study and to help students to auto-evaluate themselves. High marks to those tests will be taken into account for the final examination. Bad results to those tests are not taken into account but constitute a serious reminder.
A recapitulative interrogation (written examination) is organized during January. A student succeeding in this test will be exempted of the corresponding subjects for the final examination (in June). The expected knowledge needed for this interrogation will be officially announced during the year (usually in December).
The final examination consists of two parts: a written one and an oral one. The written part is devoted to the resolution of problems and exercises. The oral part is devoted to the theory (mainly proofs of theorems) but also includes direct applications of the theory. Once again, the expected knowledge needed for this examination will be officially announced during the year (usually in April). |
|
|
| Contacts : |
| | Part b) Analysis |
|
| S. Nicolay
Institut de Mathématique (B37), Grande Traverse, 12, Sart-Tilman, 4000 Liège.
E-mail : S.Nicolay@ulg.ac.be |
|
|
|
|
| Items online : |
Part b) Analysis
|
|
| Analyse Mathématique |
| Ces notes ont pour seule vocation d'être utilisées par les étudiants dans le cadre de leur cursus au sein de l'Université de Liège. Aucun autre usage ni diffusion n'est autorisé, sous peine de constituer une violation de la Loi du 30 juin 1994 relative au droit d'auteur. |
|
|
