### Author Topic: Problem 2  (Read 13219 times)

#### Kun Guo

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##### Problem 2
« 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?

#### Victor Ivrii

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##### Re: Problem 2
« Reply #1 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)

#### Dana Kayes

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##### Re: Problem 2
« Reply #2 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?

#### Chen Ge Qu

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##### Re: Problem 2
« Reply #3 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 = ..."?

#### Victor Ivrii

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##### Re: Problem 2
« Reply #4 on: September 28, 2012, 05:23:56 PM »
I think in the new variant (just posted) it will be more clear

#### Dana Kayes

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##### Re: Problem 2
« Reply #5 on: September 28, 2012, 08:01:03 PM »
Thanks, that makes it clear

#### Shu Wang

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##### Re: Problem 2
« Reply #6 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.

#### Victor Ivrii

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##### Re: Problem 2
« Reply #7 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

#### Thomas Nutz

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##### Re: Problem 2
« Reply #8 on: September 29, 2012, 03:37:34 PM »
should the $\phi$ in eq. 6 read $\phi(r+ct)$ rather than $\phi(x+ct)$?

#### Victor Ivrii

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##### Re: Problem 2
« Reply #9 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)

#### Jasmine Chan

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##### Re: Problem 2
« Reply #10 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?

#### Dana Kayes

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##### Re: Problem 2
« Reply #11 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?

#### Victor Ivrii

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##### Re: Problem 2
« Reply #12 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.

#### Peishan Wang

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##### Re: Problem 2
« Reply #13 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!