Algèbre et Statistique. Classe de Première B by Lebossé C., Hémery C., Faure P.

By Lebossé C., Hémery C., Faure P.

Cours conforme aux programmes du eight juin 1966.

Table des matières :

Algèbre et notions d’analyse

Leçon 1 — Vocabulaire et symboles — Notions sur les ensembles — kin binaires — purposes et fonctions
Leçon 2 — Équation du moment degré
    Somme et produit des racines
    Signe des racines
Leçon three — Trinôme du moment degré — Inéquation du moment degré — Comparaison d’un nombre aux racines d’un trinôme
Leçon four — Équations et systèmes se ramenant au moment degré
    Équations se ramenant au moment degré
    Systèmes d’équations du moment degré
    Problèmes du moment degré
Leçon five — Fonctions d’une variable réelle — Limites — Coordonnées et graphes
Leçon 6 — Dérivées — Calcul des dérivées
Leçon 7 — version des fonctions — Courbes d’équation : y = f(x)
Leçon eight — Fonctions : y = ax² et y = ax² + bx + c
Leçon nine — Fonctions : y = a/x et y = (ax + b)/(cx + d)
Leçon 10 — Fonctions : y = x³ + px + q et y = ax⁴ + bx² + c
Leçon eleven — Produit scalaire — kinfolk trigonométriques dans le triangle
Leçon 12 — Arcs et angles
Leçon thirteen — Fonctions circulaires — kinfolk fondamentales — Arcs associés
Leçon 14 — Recherche des fonctions circulaires d’un arc donné — Équations fondamentales
Leçon 15 — Formules d’addition et de multiplication — differences trigonométriques
Leçon sixteen — Dérivées des fonctions circulaires — adaptations des fonctions circulaires
Leçon 17 — l. a. droite (repère quelconque)
Leçon 18 — l. a. droite (repère orthonormé) — Le cercle
Leçon 19 — Progressions arithmétiques — Progressions géométriques
Leçon 20 — Logarithmes décimaux — utilization des tables — Calculs logarithmiques
Leçon 21 — Intérêts composés — Annuités — Échelles logarithmiques
Leçon 22 — Règle à calcul

Statistique

Leçon 1 — Généralités — examine statistique
Leçon 2 — Représentation graphique des séries statistiques
Leçon three — Éléments caractéristiques d’une série statistique
Leçon four — Indices de dispersion
Leçon five — Indices statistiques
Leçon 6 — Ajustement linéaire — Méthode des moindres carrés
Leçon 7 — Séries chronologiques
Leçon eight — Notions sur l. a. corrélation

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Extra info for Algèbre et Statistique. Classe de Première B

Sample text

But if we divide both sides by the common factor (y − 2x), then we get the previously discussed differential equation y dy = −x, dx or x+y dy = 0, dx (10) of which y = 2x is not a solution. Thus we “lose” the solution y = 2x of Eq. (9) upon its division by the factor (y − 2x); alternatively, we “gain” this new solution when we multiply Eq. (10) by (y − 2x). Such elementary algebraic operations to simplify a given differential equation before attempting to solve it are common in practice, but the possibility of loss or gain of such “extraneous solutions” should be kept in mind.

For such purposes it is necessary to measure the decay constant k. 0001216 if t is measured in years. (Matters are not as simple as we have made them appear. In applying the technique of radiocarbon dating, extreme care must be taken to avoid contaminating the sample with organic matter or even with ordinary fresh air. In addition, the cosmic ray levels apparently have not been constant, so the ratio of 14 C in the atmosphere has varied over the past centuries. ) D RUG E LIMINATION : In many cases the amount A(t) of a certain drug in the bloodstream, measured by the excess over the natural level of the drug, will decline at a rate proportional to the current excess amount.

Now find how far downstream the swimmer drifts as he crosses the river. 41. A bomb is dropped from a helicopter hovering at an altitude of 800 feet above the ground. From the ground directly beneath the helicopter, a projectile is fired straight upward toward the bomb, exactly 2 seconds after the bomb is released. With what initial velocity should the projectile be fired, in order to hit the bomb at an altitude of exactly 400 feet? 42. A spacecraft is in free fall toward the surface of the moon at a speed of 1000 mph (mi/h).

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