Download e-book for kindle: 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 — family binaires — functions 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 — edition 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 — family trigonométriques dans le triangle
Leçon 12 — Arcs et angles
Leçon thirteen — Fonctions circulaires — family fondamentales — Arcs associés
Leçon 14 — Recherche des fonctions circulaires d’un arc donné — Équations fondamentales
Leçon 15 — Formules d’addition et de multiplication — ameliorations trigonométriques
Leçon sixteen — Dérivées des fonctions circulaires — diversifications 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


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 los angeles corrélation

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Additional info for Algèbre et Statistique. Classe de Première B

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This is where the magic happens: instead of transmitting the actual value of the predicted sample, it encodes in four Beginnings 23 bits and transmits the difference between the actual and predicted samples. Because the difference from sample to sample is typically quite small, the results are generally considered to be very close to toll-quality. This fourbit transcoding process, which is based on the known behavior characteristics of human voice, enables the system to transmit 8,000 four-bit samples per second, thus reducing the overall bandwidth requirement from 64 Kbps to 32 Kbps.

The amplitude levels enable us to assign values to each of the PAM samples, although a glaring problem with this technique should be obvious to the careful reader. Very few of the samples actually line up exactly with the amplitudes delineated by the graphing process. In fact, most of them fall between the values, as shown in the illustration. It doesn’t take much of an intuitive leap to see that several of the samples will be assigned the same digital value by the coder-decoder that performs this function, yet they are clearly not the same amplitude.

This is better, but far from ideal. A better solution was needed. The better solution came about with the development of Time-Division Multiplexing (TDM), which became possible because of the transistor and integrated circuit electronics that arrived in the late 1950s and early 1960s. TDM is a digital transmission scheme, which implies a small number of discrete signal states, rather than the essentially infinite range of values employed in analog systems (the word digital literally means discrete).

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