Analyse 5 SMA

L’objectif
Acquérir les notions topologiques de base de l’espace normé Rn.
Etudier la continuité, la différentiabilité et les extremums des fonctions de plusieurs variables réelles.

Programme

Espaces vectoriels normés et topologie de Rn
Limites et continuité
Différentiabilité
Formule de Taylor et extremum

Cours PDF Exercice PDF topologie de Rn Exercice PDF Fonctions COURS Vidéos Youtube P1 COURS Vidéos Youtube P2 Exercices Vidéos (Premium) examen Vidéos (Premium)

Généralité et définitions

O n veut généraliser pour ce type de fonctions les notions et résultatsétudiés pour les fonctions réelles de la variable réelle vues, a savoir, régularité (continuité, dérivabilité ...), existence d’extrema locaux ou globaux pour les fonctions `a valeurs dans R, intégrabilité... Pour cela, il sera nécessaire de préciser certains outils topologiques déj a plus ou moins abord ́es pour l’étude des fonctions de R dans R norme, distances associée, ouvert, fermé, notion de limite ...

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