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Third Review Basic Complex Variable

1. Define what it is the residue of a meromorphic function.
2. Suppose f has a pole at to . Show that an analytic function f in the disc D (0, R) \\ {0} and suppose r is a positive number less than R , so f is bounded on D (0, r) \\ {0}. Prove that f
is analytic at zero. 4. An analytic function in open open maps. 5. Calculates the integral of-infinity to infinity of 1 / (x 2 + 30) using calculus of residues. Footer feeed

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last week

The current sign is
blue wind is now clear memories
^{now you're not}

now I'm not the greatest distance

has four words three words three words

Now is the wind

And blue is clear



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oaxaca - I

Well this week is the Joint Meeting Japan-Mexico in Oaxaca. Sali
before dawn on Saturday because a teacher kindly took us in his truck to the City, and being left there to walk with my other two friends who accompanied me in the middle. There are several interesting bookstore and bought a book by Smullyan and a couple of CDs consisting of digital versions of recordings 'classic'. One is the Ninth Symphony Beethoven, conducted by Furtwangler (1955), and other works of Gershwin are performed by André Previn.

Walking a little more than flea arrived at the Plaza of Computation and taking advantage of a little he had saved, I comrpado a Net-MD. Not yet release, and I left my laptop in Morelia and I have to update the software that brought, as it is an older version with many flaws.

barecillo Then we went to a behind the Cathedral would wait for the night. Then we go to VIPs for a coffee when I was a little later and had dinner at the socket. When the clock struck 10 pm we went to buy our Tapo tickets to Oaxaca, departing at 00:30 to sleep during the 6 hour ride (well, we try, as the truck was an oven.)

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National Olympic Complex variables

not give me time to finish ... (

2 nd Midterm Exam Complex Variable Basic. 1. Be f
analytic in a region
A
, is

w point A
, and let D (

w , R
) a disk of positive radius R A content. Then, for each z disk it holds that f (z) is the sum k from zero to infinity f (k) (w) · (zw) k / k! where f (K)
(w) represents the k-th derivative of f w
evaluated. ^{2. Articulate and demonstrate the Liouville theorem.} 3. Be f analytic in a region A and suppose there positive R such that
(
z - a
) / (1 - bz
) b where is the conjugate to , prove that r
25 comply pq + r = 2004 and pqr + 1 is a perfect square. 2. What is the highest number of positive integers that can be found so that any two of them a, b (with to than b) meet

CA in N
. Be L point on CA such that NL = AB
(and L the same side of N that A ). The line cuts ML AB in <1.

K
. Shows that KA = NC

.

4. At the end of a soccer tournament in which each pair of teams played each other exactly once and where there were no draws, it was observed that for all three teams
A, B, C
if

A
B beat and
B C defeated

, then
A beat C . Each team calculated the difference (positive) between the number of games won and lost many games. The sum of all these differences proved to be 5000. How many teams participated in the tournament? Find all possible answers. 5. Sean X, Y two circles such that the center of

O And is about X . Sean C, D the two points of intersection of the circles. Take a point in

A X and a point B in
And

such that AC is tangent to And in C and BC is tangent to A at the same point C . The segment AB cuts back to And in E , and the same segment cuts back to X in F . The line CE cut back on X G, and CF line intersects the line GD in H . Proves that the intersection of GO and EH is the center of the circumcircle of triangle DEF
.
6. What is the maximum number of direction changes in a course on the lines of a 2004x2004 grid boxes, if the route does not passes twice through the same place? feeed footer

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to understand the complete song Edith Piaf - Adieu Mon Coeur feeed footer

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French would like to know something stupid


The time is right,

your perfume fills my head reddened stars and night is so blue ... And then I go and spoil it all saying something stupid like "I love you C. Parks. I know I stand in line, until you think you have the time
To spend an evening with me
And if we go someplace to dance, I know that there's a chance
You won't be leaving with me

And afterwards we drop into a quiet little place
And have a drink or two
And then I go and spoil it all, by saying something stupid
Like: "I love you"

I can see it in your eyes, that you despise the same old lies
You heard the night before
And though it's just a line to you, for me it's true
It never seemed so right before

I practice every day to find some clever lines to say
To make the meaning come through
But then I think I'll wait until the evening gets late
And I'm alone with you

The time is right your perfume fills my head, the stars get red
And oh the night's so blue
And then I go and spoil it all, by saying something stupid
Like: "I love you"
[ mp3 ]
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We are worms, we're the best, and we've come to win the war

What Are Some Religious Quotes From Facebook

Wormsong!

Finalmente me avisaron, sí me consideraron para jurado de la Olimpiada Nacional de Matemáticas, así que visitaré Ixtapan de la Sal en unas semanas:

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What Is Ots Non Rated

I'm going to the national! Variable


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

m, with m
an integer. Exhibits

Cauchy Theorem For the special case of a square.

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