COURS de algebre 1 SMPC S1

COURS de algebre 1 SMPC S1

Chapitre :  L’espace euclidien IRn  : cliquer ici
Chapitre : Nombre complexe  : cliquer ici
Chapitre : polynome   : cliquer ici
Chapitre : Fraction Rationnelle  : cliquer ici

MODULE : ALGEBRE 1 (Cours : 21H , TD : 21H )

- Espace vectoriel euclidien
Famille libre, famille génératrice, base canonique, base orthonormée, changement de
base, formes linéaires, automorphismes orthogonaux, symétries orthogonales

- Espace affine de dimension finie
Repères, sous espaces affines, intersection de sous espaces affines, barycentres

- Géométrie dans le plan R2
Coordonnées cartésiens, coordonnées polaires, équation d’une droite, équation d’un cercle, équation d’une ellipse

- Géométrie dans l’espace R3
Coordonnées cartésiens, coordonnées cylindriques, coordonnées sphériques, équation d’une droite, équation d’un plan, équation d’une sphère

- Applications affines dans le plan R2 et dans l’espace R3
Composition, isométrie, translations, homothéties, projections, symétries

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

- Fonctions polynomiales
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

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