# Toronto Math Forum

## APM346-2012 => APM346 Math => Home Assignment 2 => Topic started by: Kun Guo on September 27, 2012, 12:45:31 AM

Title: Problem 2
Post by: Kun Guo on September 27, 2012, 12:45:31 AM
It looks like I should use the result from part 3 for part 4. However if so, how should I use the initial values?
Title: Re: Problem 2
Post by: Victor Ivrii on September 27, 2012, 11:11:15 AM
It looks like I should use the result from part 3 for part 4. However if so, how should I use the initial values?

Not really. You use parts (a),(b)
Title: Re: Problem 2
Post by: Dana Kayes on September 28, 2012, 02:50:51 PM
I'm confused about what to do when 2b) asks us to solve for v and then gives us v. I feel like I'm missing something obvious, but I can't figure it out. Can anyone help me?
Title: Re: Problem 2
Post by: Chen Ge Qu on September 28, 2012, 03:26:02 PM
I'm confused about what to do when 2b) asks us to solve for v and then gives us v. I feel like I'm missing something obvious, but I can't figure it out. Can anyone help me?

I'm also confused by this. Could it possibly mean "Solve for u using v = ..."?
Title: Re: Problem 2
Post by: Victor Ivrii on September 28, 2012, 05:23:56 PM
I think in the new variant (just posted) it will be more clear
Title: Re: Problem 2
Post by: Dana Kayes on September 28, 2012, 08:01:03 PM
Thanks, that makes it clear  8)
Title: Re: Problem 2
Post by: Shu Wang on September 29, 2012, 02:21:41 PM
for the last part, can we just assume the same solution as c) but state a few assumptions instead? it's because I dont think the general solution of the equation would vary since no other IC were stated.
Title: Re: Problem 2
Post by: Victor Ivrii on September 29, 2012, 02:36:32 PM
for the last part, can we just assume the same solution as c) but state a few assumptions instead? it's because I dont think the general solution of the equation would vary since no other IC were stated.

You should check when and if the general solution is continuous at $r=0$ and adjust it respectively
Title: Re: Problem 2
Post by: Thomas Nutz on September 29, 2012, 03:37:34 PM
should the $\phi$ in eq. 6 read $\phi(r+ct)$ rather than $\phi(x+ct)$?
Title: Re: Problem 2
Post by: Victor Ivrii on September 29, 2012, 04:01:39 PM
should the $\phi$ in eq. 6 read $\phi(r+ct)$ rather than $\phi(x+ct)$?

Yes! I fixed pdf (a bit of hassle to maintain two versions)
Title: Re: Problem 2
Post by: Jasmine Chan on September 29, 2012, 05:17:57 PM
How can I make it continuous at r=0 when I have 1/2r as part of the general solution?
Title: Re: Problem 2
Post by: Dana Kayes on September 29, 2012, 06:21:51 PM
I'm even more confused after your response to Thomas' comment - why is part b) the only part that has x as a variable now?

Could you make it clear which version you change first, so I know if I should always check the html version instead of the pdf version for changes?
Title: Re: Problem 2
Post by: Victor Ivrii on September 29, 2012, 06:34:05 PM
I'm even more confused after your response to Thomas' comment - why is part b) the only part that has x as a variable now?

Could you make it clear which version you change first, so I know if I should always check the html version instead of the pdf version for changes?

Usually changes come first to html.
Title: Re: Problem 2
Post by: Peishan Wang on September 29, 2012, 07:00:58 PM
In this question r is always positive right (since it's the distance to the origin)? Should u(r,0) and ut(r,0) be even functions of r? I guess we need additional information about u(r,0) and ut(r,0) so that v can be extended to negative values.

Thanks!
Title: Re: Problem 2
Post by: Victor Ivrii on September 29, 2012, 07:14:54 PM
In this question r is always positive right (since it's the distance to the origin)? Should u(r,0) and ut(r,0) be even functions of r? I guess we need additional information about u(r,0) and ut(r,0) so that v can be extended to negative values.

Thanks!

Title: Re: Problem 2
Post by: Chiara Moraglia on September 29, 2012, 09:49:31 PM
Sorry, I am still having trouble understanding how #2. b is asking to solve for v using v. Could someone help please?
Title: Re: Problem 2
Post by: Victor Ivrii on September 29, 2012, 11:02:40 PM
Sorry, I am still having trouble understanding how #2. b is asking to solve for v using v. Could someone help please?

We are looking for $u$, not $v$ -- but $v$ satisfies 1D wave equation and we know everything (well, almost everything) about it
Title: Re: Problem 2
Post by: Peishan Wang on September 29, 2012, 11:37:51 PM
That means in part (c) we don't need to assume that u is even and we will use this assumption in part (d)? Thanks!
Title: Re: Problem 2
Post by: Victor Ivrii on September 29, 2012, 11:53:34 PM
You are solving problem from home assignment 2, not from Strauss book. While result will be the same I see no compelling reason to assume a'priory that initial data must be even or odd.
Title: Re: Problem 2
Post by: Qitan Cui on September 30, 2012, 01:44:14 AM
Could you give some hints to part (d)? I have r in the denominator and I was thinking if I can make the numerator equal 0 when r=0, so using L'hopital rule the limit might exist. Am I on the right track? Thank you.
Title: Re: Problem 2
Post by: Victor Ivrii on September 30, 2012, 03:33:53 AM
I suspect I gave too many hints and this discussion should be stopped.