Algèbre et Analyse. Classes Terminales C, D et T by Lebossé C., Hémery C.

By Lebossé C., Hémery C.

Cours conforme aux programmes du eight juin 1966.

Table des matières :

Livre I : Ensembles fondamentaux

Leçon 1 — Ensembles — purposes et fonctions — adjustments ponctuelles
Leçon 2 — Lois de composition — buildings algébriques
Leçon three — L’ensemble N des entiers naturels — examine combinatoire
Leçon four — L’anneau Z des entiers relatifs
    Addition et soustraction
    Multiplication et division
Leçon five — Le corps Q des nombres rationnels
    Opérations sur les rationnels
Leçon 6 — Le corps R des nombres réels
    Le corps R des nombres réels
    Racines
    Interprétation géométrique des réels
Leçon 7 — Le corps C des nombres complexes
    Interprétation géométrique
    Puissances et racines
Leçon eight — functions trigonométriques de C — Équations du moment degré dans C — purposes géométriques

Livre II : Arithmétique

Leçon nine — Congruences dans Z — department euclidienne dans N
Leçon 10 — Plus grand commun diviseur — Plus petit commun multiple
Leçon eleven — Nombres premiers — functions aux fractions
Leçon 12 — Numération — Nombres décimaux

Livre III : Étude des fonctions

Leçon thirteen — Fonctions d’une variable réelle — Limites — Formes indéterminées — Fonctions continues
Leçon 14 — Dérivées — Calcul des dérivées — Dérivées successives
Leçon 15 — edition des fonctions — Courbes d’équation y = f(x) — Fonctions : y = ax² + bx + c, fonction homographique, y = ax³ + bx² + cx + d; y = ax⁴ + bx² + c
Leçon sixteen — Fonctions : y = (ax² + bx + c)/(a’x + b’), y = (ax² + bx + c)/(a’x² + b’x + c’) — Fonctions irrationnelles — Fonctions diverses
Leçon 17 — Fonctions primitives — Interprétation et purposes des primitives
Leçon 18 — Calcul de volumes
Leçon 19 — Suites de nombres réels — Progressions arithmétiques — Progressions géométriques
Leçon 20 — Fonction logarithme népérien — Logarithmes base a — Logarithmes décimaux
Leçon 21 — Fonctions exponentielles — Fonctions e^x et e^(−x) — Fonction a^x — Applications

Livre IV : Applications

Leçon 22 — Équations différentielles — Fonctions vectorielles
Leçon 23 — Calcul numérique — Tables numériques
Leçon 24 — Règle à calcul

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Additional resources for Algèbre et Analyse. Classes Terminales C, D et T

Example text

Their sole role is to compensate the unphysical degrees of contributions in the loop generated by self-interactions of the non-Abelian gauge fields in the internal lines. Unphysical contributions are generated by unphysical components, that is, scalar components of the massive gauge particle. 8b) have to be included to compensate unphysical contributions. 7 Roles of the Higgs in Gauge Theory Unitary Gauge and R-Gauge So far, we emphasized the role of the Higgs field in attaching mass to the gauge as well as matter particles.

The symmetry was not really broken, rather it was hidden as a result of choosing new variables. What is the physical meaning of the phase field? In the U-gauge, the Higgs field takes the form given in Eq. 34). Mathematically, it removes extra Higgs components beautifully which are absorbed by the gauge bosons. It can also be cast in a form given by Eq. 33) which looks more familiar. What is the difference between the two choices? Let us remember that a particle picture of the quantized field is obtained by quantizing a harmonic potential which is quadratic in the field variables.

The interaction is different depending on where and how we expand the potential. The expanded power series contains hints for the global structure of the whole potential. Inclusion of the higher order terms is to consider more global characteristics of the field which may not behave like particles. Consider, for instance, a superconducting object which we modeled in developing the Higgs formalism. It behaves as a macroscopic quantum fluid rather than as particles. The vacuum we developed as the result of the spontaneously broken symmetry is in a state of a superconducting phase.

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