COURS de Analyse SMPC S1

Objectifs

Comprendre les notions de base d'une fonction d'une variable réelle : limite , continuité , dérivabilité, développements limités.

Savoir construire des courbes paramétrées planes.

COURS Les suites COURS les fonctions COURS Développements limités

PROGRAMME

Chp. 2- Suites de nombres réels.

Définitions
Limites
Exemples remarquables
Théorème de convergence
Suites récurrentes

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

Notions de fonction
Limites Continuité en un point
Continuité sur un intervalle
Fonctions monotones et bijections
Logarithme et exponentielle
Fonctions circulaires
inverses Fonctions
hyperboliques et hyperboliques inverses
Dérivée
Calcul des dérivées
Extremum local,
théorème de Rolle
Théorème des accroissements finis

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

Formules de Taylor
Développements limités au voisinage d’un point
Opérations sur les développements limités
Applications des développements limités

COURS de Analyse MIP S1

Chapitre : Les nombres réels
Chapitre : Les suites
Chapitre : Fonctions réelles

Limites et fonctions continues
Dérivée d’une fonction

Chapitre : Développements limités

COURS de Analyse SMPC S1
Chapitre : Les suites :
Chapitre : Fonctions réelles :
Limites et fonctions continues
Dérivée d’une fonction
Chapitre : Développements limités :
Chapitre : Courbes paramétrées : cliquer ici

Analyse S1 SMPC

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