Toronto Math Forum
APM3462012 => APM346 Math => Home Assignment 2 => Topic started 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?

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)

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 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 = ..."?

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

Thanks, that makes it clear 8)

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.

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

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

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)

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

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?

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.

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!

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.

Sorry, I am still having trouble understanding how #2. b is asking to solve for v using v. Could someone help please?

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

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!

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.

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.

I suspect I gave too many hints and this discussion should be stopped.