Author Topic: Problem 2  (Read 6296 times)

Kun Guo

  • Full Member
  • ***
  • Posts: 17
  • Karma: 3
    • View Profile
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

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
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

  • Jr. Member
  • **
  • Posts: 6
  • Karma: 0
    • View Profile
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

  • Full Member
  • ***
  • Posts: 16
  • Karma: 8
    • View Profile
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

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
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

  • Jr. Member
  • **
  • Posts: 6
  • Karma: 0
    • View Profile
Re: Problem 2
« Reply #5 on: September 28, 2012, 08:01:03 PM »
Thanks, that makes it clear  8)

Shu Wang

  • Jr. Member
  • **
  • Posts: 11
  • Karma: 0
    • View Profile
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

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
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

  • Full Member
  • ***
  • Posts: 26
  • Karma: 1
    • View Profile
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

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
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

  • Newbie
  • *
  • Posts: 1
  • Karma: 0
    • View Profile
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

  • Jr. Member
  • **
  • Posts: 6
  • Karma: 0
    • View Profile
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

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
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

  • Full Member
  • ***
  • Posts: 32
  • Karma: 6
    • View Profile
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!

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: Problem 2
« Reply #14 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!

See reply #7.