Teacher(s)
Language
French
> English-friendly
> English-friendly
Prerequisites
It is recommended that the student be familiar with the basic concepts of real analysis as developed in LMAT1122 and be familiar with or in the process of becoming familiar with notions of integration in Euclidean spaces as developed in LMAT1221.
Some familiarity with the language of functional analysis as developed in LMAT1321 may be helpful, but is not essential.
Some familiarity with the language of functional analysis as developed in LMAT1321 may be helpful, but is not essential.
Main themes
The course covers the basics of measurement theory and Fourier analysis.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | At the end of this activity, students will be able to :
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Content
The course will cover elements of real analysis and harmonic analysis in Euclidean space:
- Fréchet measure and integral,
- decompositions of measures,
- integral convergence theorems,
- Fubini's and Tonelli's theorems,
- Lebesgue's differentiation theorem,
- convolution product,
- Fourier transform.
Teaching methods
The learning activities consist of lectures and practical sessions.
The lectures aim to introduce the fundamental concepts, to motivate them by showing examples and establishing results, to show their reciprocal links and their links with other courses in the Bachelor of Mathematical Sciences program.
The practical sessions aim at deepening the concepts discussed in the lecture.
The lectures aim to introduce the fundamental concepts, to motivate them by showing examples and establishing results, to show their reciprocal links and their links with other courses in the Bachelor of Mathematical Sciences program.
The practical sessions aim at deepening the concepts discussed in the lecture.
Evaluation methods
The assessment will take the form of a continuous assessment, based on mandatory assignments to be submitted throughout the term. Participation in lectures is mandatory. In the event of a second registration for the exam, the assessment will take the form of a written exam covering the entire subject.
Other information
The use of generative AI (such as ChatGPT) as a tool for writing or generating ideas for assignments is prohibited. Its use must be strictly limited to purposes such as proofreading aid or suggestions for structure, and must be explicitly mentioned in the assignment, if applicable. The student bears ultimate responsibility for the final content, and the instructor may at any time request an oral interview to verify the understanding of the concepts.
Online resources
Additional documents on Moodle.
Bibliography
Le cours sera basé sur les notes du cours du titulaire disponibles sur Moodle. L'étudiant aura l'occasion d'approfondir la matière à l'aide des extraits des références suivantes :
- R. G. Bartle, The Elements of Integration and Lebesgue Measure, Wiley, New York, 1966.
- A. Ponce. Elliptic PDEs, measures and capacities, EMS Tracts Math. 23, European Mathematical Society (EMS), Zürich, 2016
- P. Mironescu. Mesure et intégration. Polycopié parcours L3 math, Université Claude Bernard, Lyon, 2020
Faculty or entity
