Author Topic: Lecture Note 23  (Read 4490 times)

Ziting Zhou

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Lecture Note 23
« on: November 10, 2012, 05:31:01 PM »
Hi professor. I was wondering if there is a mistake in the lecture note 23. Please see the following attachment. There should be no "r" after Cn, right?

Victor Ivrii

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Re: Lecture Note 23
« Reply #1 on: November 10, 2012, 05:44:49 PM »
Right

Miranda Jarvis

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Re: Lecture Note 23
« Reply #2 on: December 18, 2012, 07:54:37 PM »
I was wondering, in lecture 23 in the explanation leading up to equation 11 it says that if considering outside the disk that we need to discard terms the are singular as r=0 is that supposed to be infinity?

Ian Kivlichan

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Re: Lecture Note 23
« Reply #3 on: December 19, 2012, 01:18:00 AM »
Miranda: it is singular insofar as it is not defined at r=0. Though it goes to infinity as r approaches 0, the value is not infinity at r=0.

Victor Ivrii

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Re: Lecture Note 23
« Reply #4 on: December 19, 2012, 02:29:42 AM »
I was wondering, in lecture 23 in the explanation leading up to equation 11 it says that if considering outside the disk that we need to discard terms the are singular as r=0 is that supposed to be infinity?

Yes, correct: we discard solutions which are singular (unbounded) as $r=\infty$. Fixed.

Miranda Jarvis

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Re: Lecture Note 23
« Reply #5 on: December 19, 2012, 05:21:48 PM »
Looking at equation 6 and 7 is this coming from equations 17 and 18 from lecture 13? using $l=2\pi$? wouldn't $\lambda$ then be $(n/4)^2$ or am I misunderstanding something?

Victor Ivrii

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Re: Lecture Note 23
« Reply #6 on: December 19, 2012, 08:43:59 PM »
No, $l=\pi$ as for periodic b.c. interval's length is $2l$ in contrast to Dirichlet or Neumann' b.c.