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 — functions et fonctions — variations 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
    Interprétation géométrique des réels
Leçon 7 — Le corps C des nombres complexes
    Interprétation géométrique
    Puissances et racines
Leçon eight — purposes trigonométriques de C — Équations du moment degré dans C — functions 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 — purposes 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 — version 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 functions 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

Sample text

The factor 1/6 comes in because the asymmetry pertains only to νe , whereas 6 types of neutrinos and antineutrinos contribute to the energy emitted. 92) To find pF , we use the leading term in Eq. 93) where Ye is the electron fraction and ρ is the mass density. Taking Ye = 1/10, we obtain 1/3 pF = 24ρ11 MeV . 94) where ρ11 is the mass density in units of 1011 g cm−3 . Putting this back in Eq. 95) where B14 = B/(1014 Gauss) and TMeV = T /(1 MeV). For Ω ≫ me which is the relevant case and S = 0 as a typical value of neutron polarization we can find out the values of the constants a and b.

35) Of course, this should not be taken as the solution for the neutrino energy, because the right hand side contains form factors which, in general, are functions of the energy and other things. But at least it shows that in the limit B → 0, the vacuum dispersion relation is recovered. If we retain the lowest order corrections in B, we can treat the form-factors to be independent of B and can write [34] 2 Ω2 = q 2 + (a22 − a23 )B2 q⊥ . 36) Calculation of this self-energy was performed by Erdas and Feldman [10] using the Schwinger propagator, where they also incorporated the modification of the W -propagator due to the magnetic field.

The calculations will be extrapolated to the case where there is a background medium also. For the medium modification of the propagators a brief discussion on statistical field theory (commonly called finite temperature field theory) is discussed in the appendix C. The Schwinger propagator is introduced in this chapter and is followed by a discussion on the phase factor accompanying it. A detailed discussion on the derivation of the Schwinger propagator is supplied in [55]. The phase factor of the Schwinger propagator is dealt in some detail.

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