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#51 2013-03-29 14:48:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

I was at a birthday party.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#52 2013-03-29 14:50:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Did you have a good time?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#53 2013-03-29 23:24:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Of course.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#54 2013-03-29 23:27:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Hmmm, you got in late enough...


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#55 2013-03-29 23:57:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Maybe.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#56 2013-03-30 00:00:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Too tired or want to continue with more problems?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#57 2013-03-30 00:02:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Well, I got my good night's sleep. We can continue.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#58 2013-03-30 00:06:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#59 2013-03-30 02:21:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

How would you do that one?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#60 2013-03-30 04:42:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Did you get the poles?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#61 2013-03-30 10:29:51

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Yes I have. -1, e^(i*pi/3) and e^(i*pi/3).


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#62 2013-03-30 11:17:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Know, which ones to use?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#63 2013-03-30 11:29:10

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Well, any contour which encloses the integral we want will do.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#64 2013-03-30 11:36:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

I guess here he used the unit circle. Anyway, only one pole...


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#65 2013-03-30 11:43:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

He?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#66 2013-03-30 11:44:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

The guy who wrote these stupid problems up. Now please find the single pole that we will use.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#67 2013-03-30 12:16:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

We can use any of the poles. But finding a contour that will do the problem will be a bit tougher.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#68 2013-03-30 12:18:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

He has got that you use only one of the poles.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#69 2013-03-30 12:20:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Who is he? And how do you know what he used?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#70 2013-03-30 12:22:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Forget about the contour, if you plug into the formula you will see that you can not use just any pole that you want.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#71 2013-03-30 12:24:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

You do realize that the 2pi*i gets the answer for a contour integral and not a regular one?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#72 2013-03-30 12:28:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

I am not sure that is correct. The answers are for the integrals that I posed. We are evaluating the integrals using residues. We only need the pole that has a positive i as the imaginary part.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#73 2013-03-30 12:30:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Are you sure you got this contour integral stuff correctly?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#74 2013-03-30 12:33:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Contour integration

Heck no! This came out of a textbook that my brother has and I do not so I jotted down the problems and the solutions. Each one is correct as far as the answer is concerned.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#75 2013-03-30 12:35:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Contour integration

Wait, so, you are just guessing?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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