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exercices corrigés de calcul différentiel sma s5

exosup

1 nov., 2018

exercices corrigés de calcul différentiel sma s5

Bernard Le Stum∗
Université de Rennes 1
Version du 28 mars 2003

contenu:
1 Fonctions différentiables, formule de la moyenne

2 Théorème des fonctions implicites, sous-variétés de Rn

3 Formule de Taylor

4 Systèmes différentiels, champs de vecteurs

5 Systèmes différentiels linéaires

exercices corrigés de calcul différentiel sma s5

Téléchargement

Nom du fichier : exercices corrigés de calcul différentiel By ExoSup.com.pdf
Taille du fichier : 348 KB
Nombre de pages : 38
Date de publication : 01/11/2018
id=1137

programme de ce module:
M29 : Module de calcul differentiel
Partie I : Espaces vectoriels normés et espaces de Banach
- Définition et exemples d’espaces vectoriels normés
- Espaces vectoriels normés de dimension finie
- Applications linéaires continues
- Applications multilinéaires continues
- Définition et exemples d’espaces de Banach
- Séries dans les espaces vectoriels normés et caractérisation de la complétude
Partie II : Calcul différentiel dans les espaces de Banach
- Définition et exemples d’applications différentiables
- Différentielle de la composée
- Différentielle d’une application à valeurs dans un espace produit
- Différentielle d’une application définie sur un espace produit, différentielle partielle
- Théorème des accroissements finis et ses applications
- Théorèmes des fonctions implicites et d’inversion locale
- Différentielle d’ordre supérieur
- Formules de Taylor
- Extremum

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