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Contrôle final Analyse 3 SMP3+Corrigé FS BenMsik

exosup

26 août, 2015

Contrôle final d'Analyse 3 SMP3+Corrigé FS BenMsik

Contrôle final Analyse 3 SMP3 2013 2014+Corrigé FS BenMsik

Université Hassan II-Mohammedia
Faculté des Sciences Ben Msik
B.P. 7955. Casablanca
SMP3- Mathématiques pour la physique 1. (2013-2014)

Contrôle final Analyse 3 SMP3 2013 2014+Corrigé FS BenMsik

Télécharger

ICI-ICI-ICI-ICI-ICI-ICI

Montrer que la fonction P(x,y) = ex cos y est harmonique sur C

Trouver le conjugué harmonique Q(x,y) pour P sur C tel que

Q(0, 0) = 0 (c’est-à-dire P + iQ est holomorphe sur C).

En déduire que f(z) = ez est holomorphe sur C.

En inégrant la fonction complexe

le demi cercle supérieur du contour

Considérons la fonction périodique de période T = 2p

Tracer dans un repère orthonormé la courbe représentative de f

Montrer que f est développable en série de Fourier

Calculer cette série

Les conditions de Cauchy-Riemann

Le théorème des résidus

La fonction f est une fonction polynomiale

f(x) est développable en série de Fourier

les coefficients de Fourier

les controles les controles SMP S3 smp smp s3

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