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Voir des cours et des Exercices Analyse 4

Séries numériques Suites et Séries de fonctions - Table de matières

Ch. I. Séries Numériques

Définitions et convergence. Séries à termes positifs et comparaison. Règles de d'Alembert, de Cauchy. Séries de Riemann. Séries à terme quelconques. Séries absolument convergentes. Séries alternées, critère d'Abel.

Ch. II. Suites et Séries de fonctions

A- Suites de fonctions : Convergences simple et uniforme. Théorèmes de continuité, dérivabilité et intégrabilité.
B- Séries de fonctions : Convergence simple, uniforme et normale. Théorèmes de continuité, dérivabilité, et intégrabilité et convergence.

Ch. III. Séries entières

Rayon de convergence. Continuité et dérivabilité de la somme. Développement en série entière des fonctions classiques.

Ch. IV. Série de Fourier

Séries Trigonométriques. Développement en série de Fourier. Théorèmes de convergences (simple, quadratique, et normale). Théorème de Dirichlet et Egalité de Perceval. Inégalité de Bessel.

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