Examen Parcial de Variabe Compleja Básica
21 de Octubre de 2004
(Fórmula integral de Cauchy) Sea C una curva cerrada y simple que yace en el interior de una región D simplemente conexa. Sea
a un punto en la región interior de C
. Demuestra que
f( a ) = (1 / 2pi
i ) Integral_C f (z ) / (z
-
to
) d z
Let G be a simple closed curve is not necessarily contained in C
\\ {- 1.1}. Determines the possible values \u200b\u200bof the integral
N = (1 / 2pi
i
) Integral_G (1 / (z
-1) (
z +1)) d z
.
Let C be the circle with center 0 and radius R. Using the definition of the integral, calculated the integral over C z
Cauchy Theorem For the special case of a square.
to
) d z
Let G be a simple closed curve is not necessarily contained in C
\\ {- 1.1}. Determines the possible values \u200b\u200bof the integral
N = (1 / 2pi
i
) Integral_G (1 / (z
-1) (
z +1)) d z
.
Let C be the circle with center 0 and radius R. Using the definition of the integral, calculated the integral over C z
m, with m
an integer. Exhibits
an integer. Exhibits
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