Тактика на мотострелковите подразделения

Начините за водене на бой на моторизираните ( БТР и различни типове бронирана транспортна техника ) части. Категория: Военна тактика

Équations de Cauchy-Riemann

Les équations de Cauchy-Riemann en analyse complexe, ainsi nommées en l'honneur d'Augustin Cauchy et Bernhard Riemann, sont deux équations aux dérivées partielles qui expriment une condition nécessaire et suffisante pour qu'une fonction soit holomorphe.

Formulation

Soit f une fonction d'un ouvert

U

\mathbb

dans

\mathbb

. En écrivant z sous la forme

z=x+iy \,

, f peut être vue comme une fonction de deux variables réelles, qu'on écrit alors : :

f(x,\, y) = P(x,\, y) + i\,Q(x,\, y)

Supposons que f soit différentiable en

z_0= (x_0,\,y_0) \,

, comme fonction de deux variables réelles. Une condition nécessaire et suffisante pour que f soit holomorphe en z₀ (c'est-à-dire dérivable par rapport à la variable complexe) est que les équations suivantes soient vérifiées : :

(x_0,\,y_0) =    (x_0,\,y_0)

(x_0,\,y_0) =  -(x_0,\,y_0)

Ces équations s'appellent équations de Cauchy-Riemann. Catégorie:Analyse complexe

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