Initiation à la théorie des distributions

Course
fr
French
27 h
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Source
  • From www.coursera.org
Conditions
  • Self-paced
  • Free Access
  • Fee-based Certificate
More info
  • 9 Sequences
  • Introductive Level

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Course details

Syllabus

Semaine 1 :
EDP d'ordre 1 et méthode des caractéristiques
L'équation de Hopf
Fonctions test
 
Semaine 2 :
Définition des distributions 
Dérivation des distributions 

Semaine 3 :
Autres opérations sur les distributions
Formule des sauts en dimension 1
Intégration sur les courbes et les surfaces 

Semaine 4 :
Formule des sauts en dimension >1 et applications 
Distributions à support compact
Convolution des distributions par des fonctions régulières 

Semaine 5 :
Régularisation des distributions 
Convolution des distributions 
Distributions tempérées 

Semaine 6 :
Transformation de Fourier sur la classe de Schwartz
Transformation de Fourier pour les distributions tempérées
 
Semaine 7 :
Introduction à l'étude des EDP
Exemples de solutions élémentaires
Détermination de quelques solutions élémentaires 

Semaine 8 :
Fonctions harmoniques 
Equation de Poisson

Semaine 9 :
Problème de Cauchy au sens des distributions
Exemples d'EDP d'évolution d'ordre 1
Un exemple d'EDP d'évolution d'ordre 2 

Prerequisite

None.

Instructors

Prof. François Golse
Professeur à l'Ecole polytechnique
Département de mathématiques

Prof. Yvan Martel
Professeur à l'Ecole polytechnique
Département de mathématiques

Editor

École Polytechnique combines research, teaching and innovation at the highest scientific and technological level in the world to meet the challenges of the 21st century. The leading French engineering school for over 200 years, its training promotes a culture of multidisciplinary scientific excellence, open to a strong humanist tradition.

It was founded in 1794 by the French National Convention under the name École centrale des travaux publics, and militarised in 1804 by Napoleon I. Originally located in Paris, the school has been in Palaiseau (Essonne) since 1976, at the heart of the Paris-Saclay technology cluster. It has the status of a public scientific, cultural and professional establishment (EPSCP-GE), is a military grande école whose engineering course is supervised by the Ministry of the Armed Forces and is a founding member of the Paris Polytechnic Institute.

Platform

Coursera is a digital company offering massive open online course founded by computer teachers Andrew Ng and Daphne Koller Stanford University, located in Mountain View, California. 

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