
Dérivation, intégration. Edition revue et augmentée
SommaireCe chapitre expose d'abord les bases du calcul différentiel dans les espaces de Banach, puis introduit les premières notions de la géométrie différentielle.Dans le paragraphe 1.1, on définit les notions d'application différentiable, de dérivée et on établit le théorème des fonctions composées (théorème 1.1.1). L'étude des fonctions à valeurs dans un produit d'espaces normes est élémentaire et se réduit à celle des fonctions composantes; l'étude des fonctions de plusieurs variables conduit à la notion de dérivée partielle (définition 1.2.1). Le paragraphe 1.3 est consacré à l'étude du théorème des accroissements finis; ce théorème est fondamental car il constitue un outil particulièrement efficace pour établir des majorations et il est utilisé dans la plupart des démonstrations de ce chapitre. Par exemple, il permet d'établir qu'une fonction admettant des dérivées partielles continues est de classe e1 (proposition 1.4.1), il permet d'étudier la différentiabilité de la limite d'une suite de fonctions différentiables (théorème 1.5.1).(...)
| Nombre de pages | 534 |
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| Date de parution | 14/04/2012 |
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| EAN | 9782705683504 |
|---|---|
| Titre | Dérivation, intégration. Edition revue et augmentée |
| Auteur | Wagschal Claude |
| Editeur | HERMANN |
| Largeur | 156 |
| Poids | 845 |
| Date de parution | 20120414 |
| Nombre de pages | 534,00 € |








