Duration
45h Th, 30h Pr
Number of credits
| Bachelor in physics | 7 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
This course constitutes the first part of the Analysis course. It introduces the fundamental methods, concepts, and tools of mathematical analysis needed in physics.
The topics covered in the course include:
- Naive set theory and basic logic
- Real and complex sequences and series
- Functions of one real variable: graphs, limits, continuity, derivatives, extrema, Taylor formula
- Functions of several real variables: limits, continuity, differentiation, extrema, Taylor formula
- Power series
Learning outcomes of the learning unit
By the end of the course, the student will have acquired a solid understanding of the fundamental concepts of mathematical analysis and will be able to apply the corresponding computational techniques. These skills can be used both in abstract settings and to solve problems arising in the physical sciences.
The student will also be able to use mathematical language to formulate, analyse, and solve simple original problems, demonstrating sound judgement and rigour in the use of the 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 "Introduction à l'enseignement universitaire de l'algèbre" course.
Planned learning activities and teaching methods
The course consists of lectures and exercise sessions.
Theoretical concepts are introduced during the lectures. The main theoretical results are then established in order to introduce and justify the tools of mathematical analysis.
The exercise sessions, supervised by teaching assistants, focus mainly on solving problems related to the theoretical material covered in the lectures. They also provide additional explanations and examples illustrating the theoretical concepts.
These two activities are complementary: mastering the techniques developed during the exercise sessions requires a solid understanding of the concepts presented in the lectures, and conversely.
Mode of delivery (face to face, distance learning, hybrid learning)
Blended learning
Further information:
The regular course schedule is available online via Celcat. Some theoretical sessions may need to be completed independently following the flipped classroom model.
Course materials and recommended or required readings
Platform(s) used for course materials:
- eCampus
Further information:
The course notes are 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 )
Further information:
The exam is written and covers all the material taught in the course, including theoretical developments (statements and proofs of results, definitions, and structured and reasoned arguments similar to those developed during the year), as well as the solving of exercises. A serious deficiency in either of these two parts (a mark below 6/20 for that part) will result in a failing grade for the course.
Work placement(s)
Organisational remarks and main changes to the course
All course-related information is available on eCampus.
Contacts
C. Esser (Celine.Esser@uliege.be)
Assistants : L. Remacle (L.Remacle@uliege.be) and E. Piette
Pedagogical Assistant: A. Lacroix (A.Lacroix@uliege.be)