algebre 1 SMPC S1

Objectifs

Acquérir les notions de calcul sur les nombres complexes. Acquérir les notions de calcul sur les polynômes à coefficients réels ou complexes.
Calcul matriciel, méthode de Gauss le calcul.
Calcul du déterminant. Géométrie du plan et de l'espace : Coordonnées cartésiens, polaires, équation de droite, cercle, ellipse, équation d'un plan, d'une sphère

COURS PDF Exercices PDF Examens PDF Exercices Vidéos (Premium) examen Vidéos (Premium) COURS Vidéos Youtube L’espace euclidien IRn COURS Vidéos Youtube Nombre complexe COURS Vidéos Youtube polynômes et fractions rationnelles

Programme

Le corps C des nombres complexes Opérations arithmétiques, conjugaison et module, exponentielle complexe, racine nième de l’unité, similitudes complexes

Polynômes à coefficients réels ou complexes Racines, dérivation, factorisation, formule de Taylor pour les polynômes, polynômes irréductibles dans R et C,

Fractions rationnelles dans R et C Pôles et zéros, décomposition en éléments simples

Opération sur les matrices, transposée d'une matrice inversible

Résolution d'un système linéaire par la méthode de Gauss

calcul du rang et de l'inverse d'une matrice par la méthode de Gauss

Cours de Algebre

Travaux dirigés de Algebre

contrôles continus Algebre

Module d'algèbre
Chapitre1 : L’espace euclidien IRn
Chapitre2 : Géométrie élémentaire dans IR2 et IR3
Chapitre3 : Nombres complexes
Chapitre4 : Polynômes
Chapitre5 : Fractions rationnelles

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