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+\usepackage{myXsim} +\usepackage{csvsimple} + +\author{Benjamin Bertrand} +\title{Données Enseignements Scientitfiques} +\date{Septembre 2020} + +%\pagestyle{empty} + +\newcommand\donnees{ + \vfill +Population du Japon + +\csvautotabular{./popjapon.csv} + \vfill + +PIB France + +\csvautotabular{./pibfrance.csv} + \vfill + +Température moyenne en France + +\csvautotabular{./temperatures.csv} + \vfill + +Nombre d'utilisateur d'internet + +\csvautotabular{./utilisateurinternet.csv} + \vfill + +} + +\begin{document} +\donnees +\donnees + +\end{document} diff --git a/EnseignementsScientifique/01_Evolution_et_démographie/exercises.tex b/EnseignementsScientifique/01_Evolution_et_démographie/exercises.tex new file mode 100644 index 0000000..c5e2fc2 --- /dev/null +++ b/EnseignementsScientifique/01_Evolution_et_démographie/exercises.tex @@ -0,0 +1,105 @@ +\collectexercises{banque} +\begin{exercise}[subtitle={Malthus}, step={3}, origin={LeLivreScolaire}, topics={Biodiversite Evolution}, tags={Suite, Modélisation}] + \noindent + \begin{minipage}{0.49\textwidth} + \begin{bclogo}[barre=none, arrondi=0.1, logo=]{Thomas Robert Malthus, Essai sur le principe de population, 1798.} + Comptons pour 11 millions la population de la Grande-Bretagne, et supposons que le produit actuel de son sol suffit pour la maintenir. Au bout de 25 ans, la population sera de 22 millions ; et la nourriture ayant également doublé, elle suffira encore à l’entretenir. Après une seconde période de 25 ans, la population sera portée à 44 millions : mais les moyens de subsistance ne pourront plus nourrir que 33 millions d'habitants. + + Dans la période suivante, la population — arrivée à 88 millions — ne trouvera des moyens de subsistance que pour la moitié de ce nombre. [...] [L’espèce] humaine croîtra selon la progression 1, 2, 4, 8, 16, 32, 64, 128, 256, etc. tandis que les moyens de subsistance croîtront selon la progression 1, 2, 3, 4, 5, 6, 7, 8, 9. + \end{bclogo} + + \begin{enumerate} + \item Détailler les deux types d'évolutions décrit par Malthus. + \item En dessinant des représentations graphiques de suites à main levée, expliquer le problème que prédit Malthus à la Grande-Bretagne. + \item Expliquer comment Verhulst améliore le modèle de Malthus. + \end{enumerate} + + \end{minipage} + \hfill + \begin{minipage}{0.49\textwidth} + \begin{bclogo}[barre=none, arrondi=0.1, logo=]{Les modèles d’accroissement démographique de Malthus et de Verhulst} + Tout comme Malthus, Verhulst créa un second modèle décrivant l’accroissement démographique d’une population donnée. Par contre, la différence majeure de l’invention de ce dernier est qu’il crée un modèle logistique intégrant dans son équation la notion de capacité limite du milieu. Cette dernière est « le nombre maximal d’individus d’une population qui peuvent vivre dans un milieu au cours d’une période donnée, sans dégradation de l’habitat ». Elle est notée K et sa valeur change selon l’abondance ou la rareté des ressources présentes dans le milieu en question. En effet, de nombreux facteurs sont limitants dans un habitat, tels que les sites appropriés de nidification, l’eau, la richesse du sol, la quantité de prédateurs, les abris adéquats et la quantité de nourriture. + \begin{center} + \includegraphics[scale=1]{./fig/logistique}\\ + \caption{Courbe de Verhulst} + \end{center} + \end{bclogo} + \end{minipage} + +\end{exercise} + +\begin{exercise}[subtitle={Transition Démographique}, step={4}, origin={Créatoin et Le libre scolaire}, topics={Biodiversite Evolution}, tags={Suite, Modélisation}] + \setlength{\columnseprule}{0pt} + \begin{multicols}{2} + \noindent + \begin{minipage}{0.5\textwidth} + \begin{bclogo}[barre=none, arrondi=0.1, logo=]{Taux d'accroissement} + Le modèle démographique de Malthus est un modèle exponentiel d’évolution de l’effectif de la population. Il peut être traduit par une suite géométrique de raison $q=1+t$ où $t$ est le taux d’accroissement de la population. Le taux d’accroissement de la population est calculé en faisant la différence entre le taux de natalité et le taux de mortalité. Ce taux peut être négatif, nul ou positif. + + \begin{center} + \includegraphics[scale=1.5]{./fig/taux} + \end{center} + \end{bclogo} + \end{minipage} + \begin{minipage}{0.5\textwidth} + \begin{bclogo}[barre=none, arrondi=0.1, logo=]{Coefficient multiplicateur et taux d'accroissement} + + \begin{minipage}{0.4\linewidth} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{}}; + \node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{}}; + + %Lines + \path[->] (leftterme.east) edge [bend left] node [above] {$\times q$} node [below] {$+t\%$} (centerterm.west); + \end{tikzpicture} + \end{minipage} + \begin{minipage}{0.5\linewidth} + $q$: coefficient multiplicateur + + $t$: taux d'accroissement + \end{minipage} + + \begin{center} + $q = 1 + t \qquad \qquad t = q-1$ + \bigskip + + avec \qquad t\% $= \frac{t}{100}$ \qquad t \textperthousand $= \frac{t}{1000}$ + \end{center} + + Exemples: + \begin{itemize} + \item Multiplier par 1,2 revient à ajouter 20\% + \item Diminuer de 30\% revient à multiplier par 0.7. + \end{itemize} + \end{bclogo} + \end{minipage} + \begin{minipage}{0.5\textwidth} + \begin{bclogo}[barre=none, arrondi=0.1, logo=]{Transition démographique} + La transition démographique est le processus historique par lequel une population passe d'un régime démographique caractérisé par un taux de mortalité et un taux de natalité élevés à un nouveau régime caractérisé par un taux de mortalité puis un taux de natalité faibles. Ce type d'évolution a été observé dans des pays d'Europe occidentale à partir de la fin du xviiie siècle, puis dans l'ensemble des autres pays au cours des trois siècles suivants, en liaison avec leur développement socio-économique. Ce processus historique explique pour l'essentiel le décuplement de la population mondiale de 1800 à 2050. + + \begin{center} + \includegraphics[scale=0.25]{./fig/transition_demo} + \end{center} + \flushright{Wikipedia} + \end{bclogo} + \end{minipage} + \end{multicols} + + \begin{bclogo}[barre=none, arrondi=0.1, logo=]{Étude démographique de l'Afrique du Sud} + Les taux suivant sont annuels et donnés en \textperthousand. + \begin{center} + \csvautotabular{./taux_afrique_sud.csv} + \end{center} + \end{bclogo} + + \begin{enumerate} + \item Compléter le tableau concernant l'étude démographique de l'Afrique du sud. + \item Identifier la phase 1 puis la phase 2 de la transition démographique de l'Afrique du Sud. + \item Sachant qu'en 1950, l'Afrique du sud comptait \np{1368300} habitants. Calculer la population en 1955 puis en 2010. + \item D'après le travail effectué, préparer un bilan sur la transition démographique d'un point de vue mathématique et démographique. + \end{enumerate} +\end{exercise} +\collectexercisesstop{banque} diff --git a/EnseignementsScientifique/01_Evolution_et_démographie/index.rst b/EnseignementsScientifique/01_Evolution_et_démographie/index.rst new file mode 100644 index 0000000..de84d14 --- /dev/null +++ b/EnseignementsScientifique/01_Evolution_et_démographie/index.rst @@ -0,0 +1,62 @@ +Evolution et démographie +######################## + +:date: 2021-09-06 +:modified: 2021-09-06 +:authors: Benjamin Bertrand +:tags: Suite, Tableur, Modélisation +:category: EnseignementsScientifique +:summary: Etude des modèles d'évolutions démographiques avec des suites. + +Étape 1: Construction d'un modèle démographique +=============================================== + +Travail de groupe pour prédire une population. Le choix du modèle n'est pas précisé. C'est aux élèves de faire les choix. + +.. image:: ./1E_demographie.pdf + :height: 200px + :alt: Prévoir et modéliser des populations + +Bilan: Les différentes croissances leur représentation graphique et les outils de calculs (variations absolue, coefficient multiplicateur et taux de variation) + +.. image:: ./1B_modeles.pdf + :height: 200px + :alt: Cours sur les suites + +Animation Géogébra: + +https://www.geogebra.org/m/vucdqkvs#material/tkecnhyc + +Étape 2: Critique d'un modèle +============================= + +En groupe les élèves choisissent un jeu de données. Ils n'étudient pas les dernières valeurs et construisent des prévisions en se basant sur les deux modèles. On leur demandera un regard critique sur les modèles. + +.. image:: ./2E_fiche_eval.pdf + :height: 200px + :alt: Fiche évaluation de l'oral + + +Étape 3: Loi de maltus +====================== + +Animation Géogébra: + +https://www.geogebra.org/m/vucdqkvs#material/rcuv9uff + +Documents pour mettre en lumière la loi de Maltus. + +.. image:: ./3E_maltus.pdf + :height: 200px + :alt: Modèle de Malthus et les ajustements + +Reprise des deux documents du livre avec une question sur la description des deux modèles rentrés. À partir d'un jeu de données, ils doivent trouver les limites des modèles exponentiel. Conclusion avec le modèle logistique. + +Étape 4: Transition démographique +================================= + +Calculs du taux d'évolution de la population à partir du taux de natalités et de mortalité, notion de transition démographique et calcul de la population de l'Afrique du sud. + +.. image:: ./4E_transition_demo.pdf + :height: 200px + :alt: Transition démographique de l'Afrique du sud diff --git a/EnseignementsScientifique/01_Evolution_et_démographie/pibfrance.csv b/EnseignementsScientifique/01_Evolution_et_démographie/pibfrance.csv new file mode 100644 index 0000000..3097c6f --- /dev/null +++ b/EnseignementsScientifique/01_Evolution_et_démographie/pibfrance.csv @@ -0,0 +1,2 @@ +Annee,1950,1952,1954,1956,1958,1960,1962,1964,1966,1968 +PIB (en milliards d'euros),15.5,22.8,25.1,29.8,38.8,47,57.1,71,83,98 diff --git a/EnseignementsScientifique/01_Evolution_et_démographie/pop_france.ods b/EnseignementsScientifique/01_Evolution_et_démographie/pop_france.ods new file mode 100644 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mode 100644 index 0000000..7579b0b --- /dev/null +++ b/EnseignementsScientifique/01_Evolution_et_démographie/temperatures.csv @@ -0,0 +1,2 @@ +Année,1998,2000,2002,2004,2006,2008,2010,2012,2014,2016 +Températures moyennes,12.53113,13.12313,13.14513,12.59113,13.23913,12.54513,11.86613,12.79113,13.72713,13.0 diff --git a/EnseignementsScientifique/01_Evolution_et_démographie/utilisateurinternet.csv b/EnseignementsScientifique/01_Evolution_et_démographie/utilisateurinternet.csv new file mode 100644 index 0000000..a7ec32b --- /dev/null +++ b/EnseignementsScientifique/01_Evolution_et_démographie/utilisateurinternet.csv @@ -0,0 +1,2 @@ +Année,1990,1992,1994,1996,1998,2000,2002,2004,2006,2008,2010,2012,2014,2016,2018 +France,0,0.2,0.6,1.7,4.1,9.3,19.6,25.4,30.5,45.9,50.2,52.9,54.4,51.5,53.3