Problem 2

[Kun Guo]

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]

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]

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]

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]

I think in the new variant (just posted) it will be more clear

[Dana Kayes]

Thanks, that makes it clear 

[Shu Wang]

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]

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]

should the $\phi$ in eq. 6 read $\phi(r+ct)$ rather than $\phi(x+ct)$?

[Victor Ivrii]

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]

How can I make it continuous at r=0 when I have 1/2r as part of the general solution?

[Dana Kayes]

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]

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]

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]

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.