Examen de algèbre 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

Examen de SMPC S1
Examen N°1
Examen N°2
Examen N°3
Examen N°4
Examen N°5
Examen N°6
Examen N°7
Examen N°8
Examen N°9
Examen N°10
Examen N°11
Examen N°12

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

Chaque chapitre se divise en deux parties : énoncés de problèmes et solutions. Nous donnons une solution complète dans la plupart des cas. Lorsqu’aucune difficulté ne devrait se présenter ou lorsqu’un problème semblable a déjà été résolu, seul une indication ou la réponse est donnée.

Très souvent, un problème admet plusieurs solutions ; nous n’en donnons qu’une en espérant que les étudiants en trouveront d’autres par eux-mêmes.

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