COURS Polynômes et Fractions rationnelles

L’objectif de ce module est de donner aux étudiants des connaissances de base en algèbre : la factorisation des polynômes, la décomposition des fractions rationnelles en éléments simples,

Algèbre des polynômes
Division des polynômes
Racines d’un polynôme
Factorisation

COURS Polynômes et Fractions rationnelles
cours N°1   cours N°2
cours N°3   cours N°4
cours N°5   cours N°6
cours N°7 cours N°8

cours N°8,5 cours N°9

cours N°9,5 cours N°10
cours N°11 cours N°12

POLYNÔMES ET FRACTIONS RATIONNELLES

L'anneau des polynômes
Définition de l'ensemble des polynômes
Polynôme formel
Valuation et degré d'un polynôme
Structures algébriques sur les polynômes
Addition de polynômes
Multiplication d'un polynôme par un élément de lK
Multiplication de polynômes
Notion d'indéterminée
Fonction polynomial
Arithmétique dans JK[X]
Division euclidienne
Divisibilité dans JK[X]
Division selon les puissances croissantes
Dérivation des polynômes
Définition d'un polynôme dérivé
Dérivées successives - formule de Taylor
Racines d'un polynôme
Définition d'une racine .
Multiplicité d'une racine .
Multiplicité d'une racine et polynômes dérivés

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