The Road to Reality
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Exercise [12.10]
http://www.roadtoreality.info/viewtopic.php?f=4&t=241
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Author:  timray60 [ 08 Jan 2009, 12:33 ]
Post subject:  Exercise [12.10]

Sameed
Here is the problem. I can't type the question adequately so I will add it to the attached.
Thanks for any help.

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File comment: Problem 12.10
Excercise 12.10.doc [22.5 KiB]
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Author:  DimBulb [ 31 Jul 2009, 17:03 ]
Post subject:  Re: Exercise [12.10]

timray60,
I did not see your solution to this exercise before I commenced my own. (I sorted the posts by subject, and because the "paper clip" sorts at the bottom I missed it)

Thanks for your explanation whydxdy is equivalent to dx \wedge dy.

I have a problem with your substitution of \theta limits of -\pi to \pi. I see how it is correct, because you have this ray or half line from the (0,0) to \infty that you are integrating over 2\pi to cover the whole plane. However, I don't see how you are getting there from your math. Could you look at my solution and tell me if you think I am wrong the way I do it?

Author:  DimBulb [ 31 Jul 2009, 23:01 ]
Post subject:  Re: Exercise [12.10]

Correction, I missed this solution because it is in the Exercise discussion forum, not Solutions.

Author:  vampirbiber [ 22 May 2010, 15:11 ]
Post subject:  Re: Exercise [12.10]

Hi,

I do have a question to this exercise, more precisely is this correct?
dx\wedge dy with x = r cos(\theta) and y = r sin(\theta) follows: dx = dr cos(\theta)-r sin(\theta)d\theta and dy = dr sin(\theta)+r cos(\theta)d\theta
now inserting this into the wedge product:
(dr cos(\theta)-r sin(\theta)d\theta)\wedge(dr sin(\theta)+r cos(\theta)d\theta) =(cos(\theta) r cos(\theta)-(-r sin(\theta) sin(\theta))) dr\wedge d\theta = r dr d\theta
because dr and d\theta are orthogonal their wedge product is a "normal" product

thanks
vb

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