2023-2024 / MATH0086-1

Analysis I, part 1


45h Th, 30h Pr

Number of credits

 Bachelor in physics7 crédits 


Céline Esser

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course represents the first part of the Analysis course, introducing the essential methods, concepts, and tools in analysis for physics.

The topics covered in the course include:

  • Naive set theory and basic logic
  • Real and complex sequences and series
  • Functions of a real variable: graph, limit, continuity, derivative, extrema, Taylor series
  • Functions of several real variables: limit, continuity, differentiation, extrema, Taylor series
  • Elementary functions: exponential and logarithm, trigonometric functions, hyperbolic functions

Learning outcomes of the learning unit

At the end of the course, the student will have a strong understanding of the fundamental concepts of mathematical analysis and will be proficient in applying the corresponding calculation techniques. These skills can be implemented in both abstract contexts and for solving practical problems within the field of physical sciences.

The student will be able to use mathematical language to formulate, analyze, and solve original and simple problems, demonstrating discernment and rigor in the use of fundamental tools of mathematical analysis.

Prerequisite knowledge and skills

Basic mathematical training acquired during secondary education is desired to approach this course with a strong foundation. Although the content is taught in detail starting from the basics, a habit of mathematical reasoning is an essential asset.

The student should master complex numbers, the summation symbol, and proof techniques presented in the "Matrix Calculation" course.

Planned learning activities and teaching methods

The course consists of lectures and exercises sessions.

Theoretical concepts are introduced during the lectures, and important theoretical results are then derived to introduce and justify mathematical analysis tools.

Exercise sessions, supervised by teaching assistants, mainly focus on solving exercises related to the content of the theoretical course. They also provide additional information and illustrative examples of theoretical concepts.

These two activities complement each other, as mastery of the techniques developed during the exercise sessions relies on a solid understanding of the concepts presented during the lectures, and vice versa.

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

Blended learning

Additional information:

The regular course schedule is available online via Celcat. Some theoretical sessions could be  completed independently - flipped classroom model.

Recommended or required readings

The course notes will be available on eCampus.

The slides used as well as the exercise lists will also be uploaded on eCampus.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Additional information:

The exam is written and covers all the material taught in the course, including theoretical developments (statements and proofs of results, definitions, structured and reasoned arguments similar to those performed during the year) and exercise solving. A serious deficiency in either of the two parts will penalize the final grade.

Work placement(s)

Organisational remarks and main changes to the course

All course-related information is available on eCampus.


C. Esser (Celine.Esser@uliege.be)

Assistants : L. Remacle (L.Remacle@uliege.be) et S. Kreczman (Savinien.Kreczman@uliege.be)

Pedagogical Assistant: A. Lacroix (A.Lacroix@uliege.be)

Association of one or more MOOCs