Lecture Note 23

[Ziting Zhou]

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]

Right

[Miranda Jarvis]

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]

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]

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]

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]

No, $l=\pi$ as for periodic b.c. interval's length is $2l$ in contrast to Dirichlet or Neumann' b.c.