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Cell[CellGroupData[{
Cell["Exercices sur le calcul d'erreur", "Subtitle",
  TextAlignment->Center],

Cell[TextData[{
  StyleBox["Exp\[EAcute]rience",
    FontSize->14,
    FontWeight->"Bold"],
  "\nVous avez mesur\[EAcute] les dimensions d'un parall\[EAcute]lipip\
\[EGrave]de. D\[EAcute]signons-les par ",
  StyleBox["a",
    FontSlant->"Italic"],
  ", ",
  StyleBox["b",
    FontSlant->"Italic"],
  ", ",
  StyleBox["c",
    FontSlant->"Italic"],
  " et notons \[CapitalDelta]",
  StyleBox["a",
    FontSlant->"Italic"],
  ", \[CapitalDelta]",
  StyleBox["b",
    FontSlant->"Italic"],
  ", \[CapitalDelta]",
  StyleBox["c",
    FontSlant->"Italic"],
  " les incertitudes affectant ces mesures. Pour des incertitudes petites \
compar\[EAcute]es aux valeurs mesur\[EAcute]es, nous ne commettons qu'une tr\
\[EGrave]s petite erreur si nous rempla\[CCedilla]ons \
l\[CloseCurlyQuote]accroissement total de la fonction par sa \
diff\[EAcute]rentielle (voir document \[LeftGuillemet] Calcul d'erreur \
\[RightGuillemet]). Dor\[EAcute]navant, nous utiliserons donc, pour calculer \
l'incertitude qui affecte un r\[EAcute]sultat, la diff\[EAcute]rentielle de \
la fonction qui lie ce r\[EAcute]sultat aux mesures. Pour les mesures que \
vous avez effectu\[EAcute]es, ces fonctions sont les suivantes :\na) la \
longueur ",
  StyleBox["l",
    FontSlant->"Italic"],
  " des ar\[EHat]tes du parall\[EAcute]lipip\[EGrave]de est donn\[EAcute]e \
par ",
  StyleBox["l",
    FontSlant->"Italic"],
  " = 4",
  StyleBox["a",
    FontSlant->"Italic"],
  " + 4",
  StyleBox["b",
    FontSlant->"Italic"],
  " + 4",
  StyleBox["c\n",
    FontSlant->"Italic"],
  StyleBox["b) la surface ",
    FontVariations->{"CompatibilityType"->0}],
  StyleBox["S",
    FontSlant->"Italic",
    FontVariations->{"CompatibilityType"->0}],
  StyleBox[" ",
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  "du parall\[EAcute]lipip\[EGrave]de est donn\[EAcute]e par ",
  StyleBox["S",
    FontSlant->"Italic"],
  " = 2",
  StyleBox["ab",
    FontSlant->"Italic"],
  " + 2",
  StyleBox["ac",
    FontSlant->"Italic"],
  " + 2",
  StyleBox["bc\n",
    FontSlant->"Italic"],
  StyleBox["c) le volume ",
    FontVariations->{"CompatibilityType"->0}],
  StyleBox["V",
    FontSlant->"Italic",
    FontVariations->{"CompatibilityType"->0}],
  StyleBox[" ",
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  "du parall\[EAcute]lipip\[EGrave]de est donn\[EAcute] par ",
  StyleBox["V",
    FontSlant->"Italic"],
  " = ",
  StyleBox["abc",
    FontSlant->"Italic"],
  ".\n\n",
  StyleBox["Utilisation du logiciel ",
    FontWeight->"Bold"],
  StyleBox["Mathematica ",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  "(ATTENTION, c'est \[AGrave] vous d'exprimer correctement les \
r\[EAcute]sultats !)\nD\[EAcute]finissons chacune de ces fonctions et \
utilisons sa diff\[EAcute]rentielle totale pour exprimer l'incertitude sur \
les r\[EAcute]sultats :"
}], "Text"],

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expression identique \[AGrave] celle donn\[EAcute]e par la r\[EGrave]gle pour \
l'addition (voir document \[LeftGuillemet] Erreur et incertitude \
\[RightGuillemet]). Calculons la longueur ",
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Cell["Et pour le volume  :", "Text"],

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    FontSize->14,
    FontWeight->"Bold"],
  StyleBox["Exercice 1",
    FontWeight->"Bold"],
  "\nAttention, la diff\[EAcute]rence des diam\[EGrave]tres donne 2 fois l'\
\[EAcute]paisseur : 26.7 - 19.5 =  7.2 mm = 2",
  StyleBox["e",
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  "\nEn appliquant la r\[EGrave]gle pour la soustraction, vous obtenez donc, \
pour l'\[EAcute]paisseur ",
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  " = 3.6 \[PlusMinus] 0.1 mm et pour la pr\[EAcute]cision ",
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}], "Text"],

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  StyleBox["Exercice 2",
    FontWeight->"Bold"],
  "\nL'aire du cercle est donn\[EAcute]e par ",
  StyleBox["S",
    FontSlant->"Italic"],
  " = \[Pi]",
  Cell[BoxData[
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  ". En appliquant la r\[EGrave]gle pour la multiplication, vous obtenez ",
  StyleBox["S",
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  " = 85.3 \[PlusMinus] 3.3 c",
  Cell[BoxData[
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  ". La pr\[EAcute]cision est fournie par l'incertitude relative ",
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  "\[TildeTilde] 3.9 %"
}], "Text"],

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  StyleBox["Exercice 3",
    FontWeight->"Bold"],
  "\nD\[EAcute]finissons les fonctions donnant le p\[EAcute]rim\[EGrave]tre \
",
  StyleBox["p",
    FontSlant->"Italic"],
  ", la surface ",
  StyleBox["S",
    FontSlant->"Italic"],
  " du sol et le volume ",
  StyleBox["V",
    FontSlant->"Italic"],
  " de la salle et utilisons les diff\[EAcute]rentielles totales pour \
calculer l'incertitude sur les r\[EAcute]sultats (ATTENTION, \[AGrave] vous \
de les exprimer correctement !)"
}], "Text"],

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    FontWeight->"Bold"],
  "\nLa masse volumique \[Rho] de l'objet est donn\[EAcute]e par le quotient \
de sa masse par son volume. En appliquant la r\[EGrave]gle pour la division, \
vous obtenez \[Rho] = 1.91 \[PlusMinus] 0.09 g/",
  Cell[BoxData[
      \(TraditionalForm\`cm\^3\)]]
}], "Text"],

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  StyleBox["Exercice 5",
    FontWeight->"Bold"],
  "\nLe volume du cylindre est donn\[EAcute] par ",
  StyleBox["V",
    FontSlant->"Italic"],
  " = \[Pi]",
  Cell[BoxData[
      \(TraditionalForm\`R\^2\)]],
  StyleBox["h",
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  ". En appliquant les r\[EGrave]gles, vous obtenez ",
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    FontSlant->"Italic"],
  " = 50.27 \[PlusMinus] 0.19 ",
  Cell[BoxData[
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  " pour le volume et \[Rho] = 7.80 \[PlusMinus] 0.03 g/",
  Cell[BoxData[
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  " pour la masse volumique"
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  "\nD\[EAcute]finissons la fonction reliant ",
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  " aux grandeurs mesur\[EAcute]es, puis calculons ",
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  " et \[CapitalDelta]",
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  " :"
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Cell[TextData[{
  "IMPORTANT. Le r\[EAcute]sultat se donne de la mani\[EGrave]re suivante :  \
",
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  " = 9.87 \[PlusMinus] 0.15 m/",
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  ". L'erreur relative vaut environ 1.5%"
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