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### Messages - Victor Ivrii

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##### APM346 Announcements / Week October 8--12: office hours of Victor Ivrii
« on: October 04, 2012, 04:30:08 AM »
Next Monday (October 8, 2012) will be no office hours (Thanksgiving)

Instead there will be Office Hours

• Tuesday (October 9) 3:00--5:00 (HU1008)
• Wednesday (October 10), 1:30--3:30 (HU1008) -- the last chance to submit HA3

All office hours in HU 1008

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##### APM346 Misc / Re: When HA marks will be available?
« on: October 03, 2012, 04:11:02 PM »
Btw..when r we suppose to see our marks for the hw?

First, don't hijack topics--your post is unrelated to "Posting solutions" topic and I moved it to a separate one.

Second, the answer to your question is obvious "When your papers are graded and marks are posted". I wish to have a bit less precise but more helpful answer, but I don't; so I give you a free advice: bug both instructors

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##### General Discussion / Registration has been tightened
« on: October 03, 2012, 01:52:18 PM »
Due to spammers--actually wannabe spammers--the were erased by admins before causing any harm--registration has been tightened: ReCaptcha has been upgraded, security questions changed and registration from Immediate became Requires email validation (next step--Requires approval by admins).

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##### APM346 Misc / Re: HW Solutions Posting on Forum
« on: October 02, 2012, 02:29:25 PM »
Thank you for your message. I agree, the policy was not enforced and it was solely my fault. On the other hand, it was not well-thought policy. So, I am setting a new one: 21:30 pm of Monday.

Next HA3 is an exemption: 21:30 Wednesday, October 10.

For Term Test 1 the rule will be: not earlier than 21:30 pm October 16 Tue.

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##### Home Assignment 2 / Problem 1--not done yet!!!
« on: October 02, 2012, 12:17:36 PM »

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##### Home Assignment 2 / Re: Problem 3
« on: October 02, 2012, 07:50:45 AM »
Again MZ solutions are perfect and it is a cut-off. Only one remark: in (b) we have even initial functions and continuation must be even due to Neumann, in (c) we have odd initial functions and continuation must be odd due to Dirichlet. So in fact in these parts the answer is obviously the same for $x>t$ and $x<t$.

RR: you obviously put the wrong limits in some of the integrals. Not that it matters for credits -- MZ got them

The rest is a flood, sorry. BTW, one can attach several docs to the post (OK, as configured currently it is up to 4 of the total size 192K). Also pdf is not the best possible format for a forum as forum does not display it: most of the browsers either cannot display pdf files or can display pdf files as standalone but not embedded into html page. *** png or jpg are better suited for a forum

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##### Home Assignment 2 / Re: Problem4
« on: October 02, 2012, 07:20:48 AM »
Guys, when someone posts a complete and correct solution it is over! There is no need to post another solution unless you can point out flaws in the original one and unless you do it on forum nobody (me including) is not going to look further.

There may be an exception (a properly typed solution is better than the best scan) but the general rule is simple: the ultimate goal of the post is a usefulness for other students. Well, in HA1 I disregarded an abdominal quality scans (snapshots) but it was because they were useless

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##### Home Assignment 2 / Re: Problem 2
« on: October 02, 2012, 07:13:01 AM »
MZ solution is OK except (d), PW solution of (d) is correct

There are my comments in 1 y.a. forum
http://weyl.math.toronto.edu:8888/APM346-2011F-forum/index.php?topic=22.msg64#msg64

$\frac{1}{r}f (ct+r)$ is an expanding spherical wave

$\frac{1}{r}g (ct-r)$ is a collapsing spherical wave (note my slightly different notations)

however both of them violate an original 3D wave equation as $r=0$ as an expanding spherical wave requires a source and a collapsing spherical wave require a sink and only for

$\frac{1}{r}\bigl[f (ct+r)-f(ct-r0\bigr])$ both source and sink cancel one another at original 3D wave equation holds in the origin as well.

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##### Home Assignment 2 / Re: Problem 1 -- not done yet!
« on: October 02, 2012, 06:56:08 AM »
Posted by: Rouhollah Ramezani
Â« on: October 01, 2012, 09:00:03 pm Â»

A) is correct

B) definitely contains an error which is easy to fix. Why I know about error? --  solution of RR  is not $0$ as $x=t$

C) Contains a logical error in the domain $\{âˆ’2t<x<2t\}$ (middle sector) which should be found and fixed. Note that the solution of RR there is not in the form $\phi(x+2t)+\psi(x-2t)$

RR deserves a credit but there will be also a credit to one who fixes it

So, for a wave equation with a propagation speed $c$ and moving boundary (with a speed $v$) there are three cases (we exclude exact equalities $c=\pm v$ ) -- interpret them as a piston in the cylinder:
• $-c<v<c$ The piston moves with a subsonic speed: one condition as in the case of the staying wall
• $v>c$ The piston moves in with a supersonic speed: no conditions => shock waves etc
• $v<-c$ The piston moves out with a supersonic speed: two conditions.
3D analog: a plane moving in the air. If it is subsonic then everywhere on its surface one boundary condition should be given but for a supersonic flight no conditions on the front surface, one on the side surface and two on the rear (with $\vec{v}\cdot \vec{n} >c$, $-c< \vec{v}\cdot \vec{n} <c$ and $\vec{v}\cdot \vec{n} <-c$ respectively where $\vec{v}$ is the plane velocity and $\vec{n}$ is a unit outer normal at the given point to the plane surface. The real fun begins at transonic points where $\vec{v}\cdot \vec{n} =\pm c$).

PS MathJax is not a complete LaTeX and does not intend to be, so it commands like \bf do not work outside of math snippets (note \bf); MathJax has no idea about \newline as it is for text, not math. For formatting text use either html syntax (in plain html) or forum markup

PPS \bf is deprecated, use \mathbf instead

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##### Home Assignment 3 / Re: Problem5
« on: October 01, 2012, 10:42:19 PM »
I thought for a heat equation there is max principle in general. Is this happening because the coefficient is x but not another random variable? Thanks

The truth is that it is not a heat equation as coefficient at $u_{xx}$ is not everywhere positive

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##### Home Assignment 1 / Re: WTH?
« on: October 01, 2012, 10:39:39 PM »
BTW, has anyone any idea how much time it takes to prepare 1 hour of lecture notes or 1 home assignment? 2-3 hours :-)

I started using vim recently in an effort to type TeX commands faster. But it has a steep learning curve

I am not sure if vim speeds things up. I am using Mou (MacOSX markdown editor with real time preview and html export), still slow

2472
##### Home Assignment 2 / Re: Problem4
« on: October 01, 2012, 02:58:36 PM »
hi y'all, a quick question,
would it be appropriate to assume x & t are independent variables in this question? as like, they are presumably not correlated in any function of each other.

Also, what does it mean by rho = T = 1 ? (is T the the kinetic energy or something?)

When modeling a physical string, $T$ represents the tension force and $\rho$ is the mass density. I think they are just asking us to consider $c = 1$ for this problem, since $c = \sqrt{\frac{T}{\rho}}$.

$\rho$ is the linear mass density. On the first question: yes, $x,t$ are independent variables ($t$ is a time and $x$ is a spatial coordinate)

2473
##### APM346 Misc / Re: Where to buy the Strauss textbook w/ solutions?
« on: September 30, 2012, 11:35:00 PM »
The U of T bookstore doesn't seem to have it in stock. All they had was a textbook by Lawrence Evans which seemed much too advanced.

Evans book is a graduate textbook and very popular but I am not too excited and find it boring.

Neither I am very excited about Strauss book. One can buy from Amazon.ca

2474
##### Misc Math / Re: Classification criteria for PDEs
« on: September 30, 2012, 11:31:47 PM »
Yes if matrix of the corresponding coefficients is non-degenerate, the l.o.t. are of no importance and classification depends only on the sign of discriminant $B^2-4AC$. However if discriminant is 0, l.o.t. play role. Your equation is hyperbolic and you can find characteristics.

Also there are profound differences between hyperbolic equations with 2 independent variables like $u_{tt}-u_{xx}=0$ and with $n\ge 3$  independent variables like $u_{tt}-u_{xx}-u_{yy}=0$.

2475
##### Home Assignment 2 / Re: Problem4
« on: September 30, 2012, 12:13:59 PM »
Are we allowed in part "a" to use initial wave equation for equality proof? ([d^2u/dt^2-d^2u/dx^2=0] in de/dt=dp/dx and de/dx=dp/dt (partials) )