# Toronto Math Forum

## APM346-2012 => APM346 Math => Misc Math => Topic started by: Ziting Zhou on November 10, 2012, 05:31:01 PM

Title: Lecture Note 23
Post by: Ziting Zhou 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?
Title: Re: Lecture Note 23
Post by: Victor Ivrii on November 10, 2012, 05:44:49 PM
Right
Title: Re: Lecture Note 23
Post by: Miranda Jarvis 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?
Title: Re: Lecture Note 23
Post by: Ian Kivlichan 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.
Title: Re: Lecture Note 23
Post by: Victor Ivrii 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.
Title: Re: Lecture Note 23
Post by: Miranda Jarvis 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?
Title: Re: Lecture Note 23
Post by: Victor Ivrii 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.