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Messages - Peishan Wang

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Home Assignment 3 / Re: Problem 6
« on: October 08, 2012, 08:05:08 AM »
Professor can we assume that u is 0 at positive and negative infinity? Thanks!

Home Assignment 3 / Re: problem 3
« on: October 08, 2012, 07:43:01 AM »
Should part (c) and part (d) be: solve the IBVP for x>0 or for all x? Thanks!

Home Assignment 3 / Re: Problem 2
« on: October 08, 2012, 06:04:48 AM »
Professor for part (b), is there any restriction on when we can use method of reflection (continuation) to solve IBVP? Thanks!

Home Assignment 2 / Re: Problem 3
« on: October 01, 2012, 09:13:46 PM »
Should we consider solutions on different intervals (i.e. x>2t and 0<x<2t) since they differ in part (a) and part (d)?

Home Assignment 2 / Re: Problem 2
« on: October 01, 2012, 09:08:02 PM »
Used a different way to do part (d)

Home Assignment 2 / Re: Problem 2
« 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!

Home Assignment 2 / Re: Problem 2
« 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.


Home Assignment 2 / Re: problem 1 typo?
« on: September 29, 2012, 03:08:00 PM »
Professor I have a question for part (c). Does the solution have to be continuous? For example I have f(x) on x>2t, g(x) on -2t<x<2t and h(x) on -3t<x<-2t. Should f(2t) = g(2t) and g(-2t)=h(-2t) (so the overall solution is continuous)?

My problem is that some of the f, g, h involve a constant K and I was wondering if I should use continuity to specify what K is.

Thanks a lot!

Home Assignment 2 / Problem 3
« on: September 26, 2012, 04:28:16 AM »
Part (a) and (b), part (c) and (d) the same questions? Thanks

Home Assignment 1 / Re: Problem 5
« on: September 26, 2012, 04:22:17 AM »
OMG I didn't realize there was a correction on Sep 23! I finished the assignment on Friday night and didn't expect that there would be any change to the questions just several hours before the assignment is due....

Professor can you give some consideration to the situation this time?

Home Assignment 1 / Re: Problem 5
« on: September 26, 2012, 04:12:44 AM »
Professor I used a similar method but got the final answer completely different (see attached).
In the equation ϕ(0)+ψ(−6t)=2t, shouldn't we have ψ'(−6t) since the second initial condition gives du/dt?

Home Assignment 1 / Re: Problem 4
« on: September 26, 2012, 03:53:33 AM »
Using polar coordinates would make things much easier (see attachments). However we need to be careful here since arccos gives us the angle from 0 to pi. When y<0 (i.e. theta > pi), it will become 2pi - arccos.

Please let me know if there's anything wrong with my posted solution.

Home Assignment 1 / Re: Problem 4
« on: September 23, 2012, 04:04:44 AM »
I followed the normal steps and found the general solutions to both equations. I cannot figure out why one of them do not exist. Is it because some function is not defined? Get lost in part (c)...

Home Assignment 1 / Re: Problem 4
« on: September 21, 2012, 08:38:37 PM »
From the auxiliary equations dx/a=dy/b=du/f, we can either express du in terms of dx and integrate over x, or express du in terms of dy and integrate over y. But sometimes these two approaches give different results. Then can we say that the general solution does not exist?

Home Assignment 1 / Re: Problem 2
« on: September 21, 2012, 07:19:46 PM »
Thank you for your hint but I still didn't get the point..

For example if the general solution has the form f(x/y), how can I make them continuous at (0,0)? Thanks!!

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