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3D\begin{figure}\vskip-1cm\hskip-1cm\psfig{file=3DFigures/ucbl.ps,rhe=

DEUG Sciences et Technologies=20

SM UE 11 : Math=E9matiques=20

COURS et EXERCICES=20

=20



  • Sommaire=20
  • Nombres complexes=20
    • D=E9finitions et op=E9rations=20
      • L'ensemble des nombres complexes=20
      • Op=E9rations fondamentales sur les nombres = complexes=20
      • Module d'un complexe
    • Repr=E9sentation g=E9om=E9trique des nombres = complexes=20
    • Racines n-i=E8mes de l'unit=E9=20
    • R=E9solution des =E9quations du second degr=E9 =
    • Fondements axiomatiques de la th=E9orie des = nombres complexes=20 (Hamilton, 1835)=20
    • Exercices sur les nombres complexes=20
    • Test de 30 mn sur les nombres complexes (Automne = 2000)=20

  • Fonctions circulaires et fonctions circulaires = r=E9ciproques=20
    • Fonctions circulaires : formulaire=20
      • Formules =E9l=E9mentaires=20
      • Formules d'addition=20
      • Formules de duplication=20
      • Formules de lin=E9arisation=20
      • Formules de factorisation=20
      • Formules relatives aux angles associ=E9s=20
      • Quelques valeurs particuli=E8res
    • Fonctions circulaires r=E9ciproques=20
    • Compl=E9ments pour le calcul des 3D"$, 3D"$, 3D"$ de r=E9els=20
      • Comment calculer et  ?=20
      • Comment calculer  ?=20
      • Comment calculer , et  ?=20
      • Comment calculer , et  ?=20
      • Comment calculer et  ?
    • Exercices sur les fonctions circulaires et les = fonctions=20 circulaires r=E9ciproques=20
      • Fonctions circulaires=20
      • Fonctions circulaires r=E9ciproques =
    • Test de 30 mn sur les fonctions circulaires = r=E9ciproques=20 (Automne 2000)

  • Fonctions exponentielles, logarithmiques et = hyperboliques=20
    • Fonctions exponentielles et logarithmes=20
      • Rappel de propri=E9t=E9s alg=E9briques = fondamentales du=20 logarithme et de l'exponentielle=20
      • Graphes des fonctions exponentielle et = logarithme=20
    • Fonctions exponentielles=20
      • Graphes des fonctions exponentielles
      • Graphes des fonctions puissances
    • Fonctions logarithmiques=20
      • Graphes des fonctions logarithmiques =
    • Comparaison de la croissance des fonctions 3D"$, 3D"$ et =20
    • Fonctions hyperboliques=20
      • Relations fondamentales=20
      • Formules d'addition=20
      • Formules de duplication=20
      • D=E9riv=E9es=20
      • Limites aux bornes des intervalles de = d=E9finitions=20
      • Graphes des fonctions hyperboliques =
    • Exercices sur les fonctions exponentielles, = logarithmes et=20 hyperboliques=20
      • Fonctions exponentielles et logarithmes=20
      • Fonctions hyperboliques
    • Test de 30 mn sur les fonctions hyperboliques = (Automne=20 2000)

  • Limites de fonctions et fonctions continues=20
    • Limite d'une fonction en un point=20
      • Quelques D=E9finitions=20
      • Propri=E9t=E9s des limites=20
      • Fonctions =E9quivalentes
    • Fonctions continues=20
      • D=E9finitions=20
      • Propri=E9t=E9s des fonctions continues=20
      • Fonctions continues strictement monotones sur un = intervalle
    • D=E9riv=E9es et limites=20
      • d=E9finitions=20
      • utilisation des d=E9riv=E9es pour le calcul des = limites=20
    • Exercices sur les limites de fonctions et les = fonctions=20 continues=20
    • Test de 45 mn sur les limites de fonctions et les = fonctions=20 continues (Automne 2000)

  • fonctions d=E9rivables et leurs d=E9riv=E9es=20
    • D=E9finitions et propri=E9t=E9s=20
      • d=E9finitions=20
      • propri=E9t=E9s des fonctions d=E9rivables et des = d=E9riv=E9es=20
    • Calcul de d=E9riv=E9es=20
    • Formule des accroissements finis et = applications=20
      • Formule des accroissements finis=20
      • Applications
    • D=E9riv=E9es successives. Formule de Taylor=20
      • d=E9riv=E9es d'ordre sup=E9rieur =E0 1
      • formule de Taylor
    • Exercices sur les fonctions d=E9rivables et leurs = d=E9riv=E9es=20
    • Test de 30 mn sur les fonctions d=E9rivables et = leurs d=E9riv=E9es=20 (Automne 2000)

  • D=E9veloppements limit=E9s=20
    • D=E9finitions et propri=E9t=E9s=20
      • D=E9finitions=20
      • Quelques propri=E9t=E9s des d=E9veloppements = limit=E9s=20
    • Calcul des d=E9veloppements limit=E9s en 0=20
      • Cas particuliers=20
      • Op=E9rations sur les d=E9veloppements limit=E9s = en 0=20
      • D=E9veloppements limit=E9s en 0 de fonctions = usuelles=20
    • Applications des d=E9veloppements limit=E9s=20
      • Calcul de limites=20
      • Calcul de d=E9riv=E9es successives d'une = fonction en un=20 point=20
      • Recherche d'asymptote pour le graphe d'une = fonction=20
    • Exercices sur les d=E9veloppements limit=E9s=20
    • Exercices suppl=E9mentaires avec r=E9ponses = sur les=20 d=E9veloppements limit=E9s et le calcul de limites=20
    • Partiel (Automne 2000)

  • Primitives et int=E9grales=20
    • Introduction=20
    • D=E9finitions et premi=E8res propri=E9t=E9s=20
    • Liste des primitives usuelles=20
    • Exercices sur les primitives et int=E9grales=20
      • Int=E9gration par parties=20
      • Changements de variables=20
      • Primitives et Int=E9grales des fractions = rationnelles=20
      • Primitives et int=E9grales des fonctions = circulaires=20
      • Autres exercices... =

  • Equations diff=E9rentielles=20
    • Equations diff=E9rentielles =E0 coefficients = constants=20
      • Equations du premiere ordre du type 3D"$ avec 3D"$ r=E9el=20
      • Equations du second ordre du type 3D"$ avec 3D"$ r=E9el=20
      • Equations du second ordre du type 3D"$ avec 3D"$ r=E9els=20
      • Equation 3D"$=20
        • M=E9thode de r=E9solution=20
        • Recherche d'une solution particuli=E8re=20
        • Cas o=F9 le second membre est somme de = fonctions=20
    • Equations diff=E9rentielles du premier ordre=20
      • Exemple=20
      • Equation lin=E9aire =20
        • Equation 3D"$=20
        • Equation 3D"$ :=20 3D"$
      • Exemples d'autres =E9quations = diff=E9rentielles=20
        • Equations =E0 variables s=E9par=E9es=20
        • Equations homog=E8nes =
    • Exercices sur les =E9quations = diff=E9rentielles=20
    • Test de 30 mn sur les =E9quations = diff=E9rentielles (Automne=20 2000)

  • Courbes param=E9tr=E9es=20
    • G=E9n=E9ralit=E9s, d=E9finitions, exemples=20
      • D=E9finitions=20
      • Exemples=20
      • D=E9finitions=20
      • D=E9finition : d=E9veloppement = limit=E9
    • Plan d'=E9tude d'une courbe param=E9tr=E9e=20
      • Domaine d'=E9tude=20
      • Tableau de variation=20
      • Etude locale=20
      • Etude des branches infinies=20
      • Repr=E9sentation graphique=20
      • Remarques:
    • Etude d'une courbe param=E9tr=E9e : =E9tude = locale=20
      • Tangente en 3D"$=20
      • Etude dans le cas o=F9 3D"$ et 3D"$ ne sont pas = colin=E9aires=20
      • Etude locale, autres cas
    • Branches infinies, asymptotes=20
    • Exercices sur les courbes param=E9tr=E9es=20
    • Epreuve de Math=E9matiques, Deug SM, Deug STI, = UE11, janvier=20 2001 (3 Heures)

  • Corrections
    • Correction du test de 30 mn sur les nombres = complexes=20 (Automne 2000)=20
    • Correction du test de 30 mn sur les fonctions = hyperboliques=20 (Automne 2000)=20
    • Correction du test de 45 mn sur les limites de = fonctions et=20 les fonctions continues (Automne 2000)=20
    • Correction du test de 45 mn sur les fonctions = d=E9rivables et=20 leurs d=E9riv=E9es (Automne 2000)=20
    • Correction du partiel=20
    • Correction du test de 1h sur les primitives et = les=20 =E9quations diff=E9rentielles (Automne 2000)=20
    • Correction de l'=E9preuve de Math=E9matiques, = Deug SM, Deug=20 STI, UE11, janvier 2001 (3 Heures)=20
    • .

  • About this document ...


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