2020-2021 / MATH0071-1

Analysis I, part 1

Part I

Part 2

Duration

Part I : 35h Th, 20h Pr
Part 2 : 10h Th, 10h Pr

Number of credits

 Bachelor in mathematics8 crédits  

Lecturer

Part I : Samuel Nicolay
Part 2 : Samuel Nicolay

Coordinator

Samuel Nicolay

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

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,...).

Part I

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,...).

Part 2

This course contains proofs and theoretical notions that complete the course MATH0071-A-a.

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.

Part I

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

Part 2

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

Prerequisite knowledge and skills

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

Part I

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

Part 2

The notions presented in the course MATH0071-A-a will be completed. It is thus necessary to master these notions as the course goes along.

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.

Part I

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.

Part 2

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.

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.

Part I

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.

Part 2

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.

Organisational adjustments related to the current health context

Part I

In case of restrictions related to a health crisis, the exams can be adapted in order to respect the imposed constraints. Face-to-face exams will be given preference. If it is not possible, the questions will be sent using webmail. Concerning the students in Mathematics, the oral exam will be conducted using a software similar to Lifesize.

Part 2

In case of restrictions related to a health crisis, the exams can be adapted in order to respect the imposed constraints. Face-to-face exams will be given preference. If it is not possible, the questions will be sent using webmail. Concerning the students in Mathematics, the oral exam will be conducted using a software similar to Lifesize.

Recommended or required readings

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

Part I

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

Part 2

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

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.

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.

Part I

See the course MATH0071 corresponding to the degree.

Part 2

See the course MATH0071 corresponding to the degree.

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.

Part I

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.

Part 2

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.

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

Part I

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

Part 2

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