### Duration

45h Th, 30h Pr

### Number of credits

Bachelor in mathematics | 8 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

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 complex plane. We will then consider the functions and their properties (continuity, derivation,...).

Mathematical analysis is the branch of mathematics concerned with the concept of limit. In this course, we will introduce the concept of the limit of a sequence in the complex plane. Subsequently, we will explore functions and their properties, including continuity and differentiation.

### Learning outcomes of the learning unit

The aim of this course is to introduce the basic notions and results concerning the mathematical analysis for one variable functions.

The aim of this course is to introduce the basic notions and results concerning the mathematical analysis for one variable functions.

### Prerequisite knowledge and skills

Only knowledge in Elementary mathematics is required. Of course, abilities to mathematical reasoning are an asset.

Only a foundational understanding of elementary mathematics is required. However, having strong mathematical reasoning abilities is an advantageous asset.

### Planned learning activities and teaching methods

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.

The exercises, supervised by the assistants, primarily focus on solving problems related to the theory covered in the course. They also serve as a valuable resource for gaining additional insights and illustrating concepts introduced in the theoretical part of the course.

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

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.

Face-to-face course

*Additional information:*

The timetable will be made available at the start of the academic year. Regarding the exercises, a comprehensive schedule and information about how students will be grouped will also be provided.

### Recommended or required readings

There is a reference book. Partial course notes (in french) are also available. The slides will also be made available.

A reference book is available, and you can also access partial course notes in French. Additionally, we will provide access to the course slides.

### Assessment methods and criteria

**Exam(s) in session**

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

**Other : No oral exams for the physical sciences.**

*Additional information:*

Concerning the students in the Mathematic Bachelor Degree. The examination consists of two parts: a written one and an oral one, except for the students attempting the agregation (these will not have any oral part). 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. If a result (considered without decimal numbers) is lower than 8/20 in one of the parts, the lowest result will contribute for two third of the total result. Otherwise, both parts will contribute equally to the final result. The expected knowledge needed for this examination will be officially announced during the year.

**Exam(s) in session**

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

*Additional information:*

The examination consists of two parts: a written section and an oral section, except for students attempting the aggregation (these students will not have an oral component). The written section is focused on solving problems and exercises, while the oral section covers theory, primarily proofs of theorems, but also includes practical applications of the theory. If a score (considered without decimal numbers) falls below 8/20 in one of the sections, the lowest score will count for two-thirds of the total score. Otherwise, both sections will contribute equally to the final score. The expected knowledge required for this examination will be officially announced during the year.

### Work placement(s)

### Organizational remarks

In case of restrictions related to a health crisis, the teaching can be adapted in order to respect the imposed constraints. For example the flipped classroom strategy could be adopted.

In the event of restrictions due to a health crisis, the teaching approach can be adjusted to comply with the imposed constraints. For instance, we may adopt the flipped classroom strategy.

### Contacts

S. Nicolay
Institut de Mathématique (B37), Grande Traverse, 12, Sart-Tilman, 4000 Liège.

E-mail : S.Nicolay@uliege.be

Site web : www.afaw.ulg.ac.be

S. Nicolay
Institut de Mathématique (B37), Grande Traverse, 12, Sart-Tilman, 4000 Liège.

E-mail: S.Nicolay@ulg.ac.be

Website: www.afaw.ulg.ac.be