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#51 2013-03-30 13:48:12

anonimnystefy
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Re: Contour integration

I was at a birthday party.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#52 2013-03-30 13:50:13

bobbym
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Re: Contour integration

Did you have a good time?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#53 2013-03-30 22:24:22

anonimnystefy
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Re: Contour integration

Of course.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#54 2013-03-30 22:27:06

bobbym
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Re: Contour integration

Hmmm, you got in late enough...


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#55 2013-03-30 22:57:41

anonimnystefy
Real Member

Offline

Re: Contour integration

Maybe.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#56 2013-03-30 23:00:55

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#57 2013-03-30 23:02:21

anonimnystefy
Real Member

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Re: Contour integration

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#58 2013-03-30 23:06:42

bobbym
Administrator

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Re: Contour integration


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#59 2013-03-31 01:21:42

anonimnystefy
Real Member

Offline

Re: Contour integration

How would you do that one?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#60 2013-03-31 03:42:09

bobbym
Administrator

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Re: Contour integration

Did you get the poles?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#61 2013-03-31 09:29:51

anonimnystefy
Real Member

Offline

Re: Contour integration

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#62 2013-03-31 10:17:49

bobbym
Administrator

Offline

Re: Contour integration

Know, which ones to use?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#63 2013-03-31 10:29:10

anonimnystefy
Real Member

Offline

Re: Contour integration

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#64 2013-03-31 10:36:08

bobbym
Administrator

Offline

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#65 2013-03-31 10:43:44

anonimnystefy
Real Member

Offline

Re: Contour integration

He?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#66 2013-03-31 10:44:50

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#67 2013-03-31 11:16:08

anonimnystefy
Real Member

Offline

Re: Contour integration

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#68 2013-03-31 11:18:28

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#69 2013-03-31 11:20:05

anonimnystefy
Real Member

Offline

Re: Contour integration

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#70 2013-03-31 11:22:26

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#71 2013-03-31 11:24:29

anonimnystefy
Real Member

Offline

Re: Contour integration

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#72 2013-03-31 11:28:59

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#73 2013-03-31 11:30:42

anonimnystefy
Real Member

Offline

Re: Contour integration

Are you sure you got this contour integral stuff correctly?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#74 2013-03-31 11:33:29

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#75 2013-03-31 11:35:41

anonimnystefy
Real Member

Offline

Re: Contour integration

Wait, so, you are just guessing?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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