Analyse 1 MIP (SMIA )

Cours de Analyse

Travaux dirigés de Analyse

Examen de Analyse

programme analyse

L’objectif de ce module est de familiariser les étudiants avec le vocabulaire ensembliste, de donner des différentes méthodes de convergence des suites réelles et les différents aspects de l’analyse des fonctions d’une variable réelle.

PROGRAMME

Chp. 1- Les nombres réels.

Relations d’ordre sur IR. Valeur absolue. Axiomes de la borne supérieure. Caractérisation de la borne supérieure. Borne inférieure. Caractérisation de la borne inférieure. Conséquences : la partie entière d’un nombre réel, densité des nombres rationnels et irrationnels.

Chp. 2- Suites de nombres réels.

Suites majorées, minorées, bornées. Suites convergentes. Suites adjacentes. Théorème des segments emboités. Sous-suites d’une suite. Propriétés des sous-suites. Théorème de Bolzano-Wierstrass. Notion de Suites de Cauchy

Chp. 3- Fonction d’une variable réelle

Limites et continuité. Dérivabilité, Théorèmes de Rolle et des accroissements finis.

Chp. 4- Formule de Taylor, développements limités et applications

Formule de Taylor et développements limités. Applications à l’étude des fonction

Analyse S1 SMIA

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