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Messages - Victor Ivrii

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2446
Home Assignment 1 / Re: Problem 2
« on: September 22, 2012, 10:31:22 PM »
I am not sure what does it mean by 'explain the difference'. Is it the difference between the solutions or the condition under which they are continuous at (0,0)?

The solutions of (a) and (b) are drastically different. Why?

2447
Home Assignment 1 / Re: Problem 3
« on: September 22, 2012, 02:33:13 PM »
I did use the method of characteristics, but I parametrized x and y in terms of s and integrated with respect to s . The thing is my solution doesn't depend on Y, is this ok ?

I have no idea what is $s$. TA who will check your paper probably has no idea either. You need to return to the original coordinates $x,y$.

2448
Home Assignment 1 / Re: Problem 3
« on: September 22, 2012, 01:45:48 PM »
Hello,

For this question I managed to find a solution that satisfies the conditions, but that only depends on X and a constant.

In general, if I find a solution that satisfies all conditions is this solution correct regardless of the method used to find it?

You need to find all solutions and justify that there are no other solutions. The method of characteristics we studied ensures this if correctly applied. Your home-brewed method may not.

2449
Home Assignment 1 / HA1-pdf
« on: September 22, 2012, 01:40:44 PM »
Here is HA1.pdf - Home assignment 1 printed to pdf (updated Mon 24 Sep 2012 05:03:22 EDT)

2450
APM346 Misc / Re: about the MathJax
« on: September 22, 2012, 12:47:24 PM »
i had try to follow the instruction below but don't know wehre to find <head> or <body> code so i can insert the code to.

...snip...

To see how to enter mathematics in your web pages, see Putting mathematics in a web page below.

You do not need to follow the instructions you copied, they are for hooking up MathJax and we did it.


Since you do not see a properly rendered math, I presume that something is wrong with your set-up

What is your OS?
What is your web browser?
Is Javascript enabled?
If you use laptop, or handheld can you come with it to my office during office hours?




2451
Home Assignment 1 / Re: Problem 2
« on: September 22, 2012, 12:40:30 PM »
Hi, for number 2, say we get $u = f(g(x,y))$ for our general solution when $(x,y) \ne (0,0)$. Then are we just finding a $u(0,0)$ that is equal to the limit of $u = f(g(x,y))$ as $(x,y)$ approaching $(0,0)$ in order to make u continuous at $(0,0)$?

Well, you need to be sure that this limit exists, right?

2453
Misc Math / Re: characteristic vs. integral lines
« on: September 22, 2012, 02:20:38 AM »
I feel like I understand what is being said here, but I am confused by the second set of lecture notes,  specifically equation (7) which seems to be doing the same thing as equation (4) in the reply to this post except with a + sign instead of a equal. Am I misunderstanding and these are actually different scenarios, or is one a misprint?

Miranda, thanks!  There was a misprint (mistype) in Lecture 2 (equation (7)), should be =.
Now it has been corrected.

2454
Home Assignment 1 / Re: Problem 4
« on: September 22, 2012, 02:15:54 AM »
In this settings you need to select a solution having certain properties

It may happen that

  • Is what one expects
  • Unusually broad
  • Unusually narrow

Your task is to determine what happens here.

2455
APM346 Misc / Re: about the MathJax
« on: September 22, 2012, 02:12:11 AM »
where can I find the code from my document to start from OR to insert the copied code from the MathJax website to?



What do you want and what is your problem?
  • Do you see mathematical expressions I typed on our forum properly?
    • Yes
    • No
  • Have you troubles typing math by yourself?
    • Yes
    • No
  • Are you trying to set MathJax somewhere else?
    • Yes
    • No

Only in the last case you need to worry about setting MathJax.

Please do not flood!!!

2456
Home Assignment 1 / Re: Problem 2
« on: September 21, 2012, 07:30:41 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 it continuous at (0,0)? Thanks!!

You are almost done (but check the general solutions!) Think - and don't post solutions!!!

2457
Misc Math / Re: characteristic vs. integral lines
« on: September 21, 2012, 06:36:18 PM »
Heythere,
I am confused by the terms characteristic lines and integral lines. The book introduces characteristic lines as the curves along which a function is constant. Now in the notes integral lines are curves to which the vector field is tangential, i.e. in the case of the gradient vector field the lines along which the function changes most (in abs. value).

So I thought these two should be orthogonal in the case of $au_t+bu_x=0$.
So are integral lines the same as characteristic lines?

If we consider 1-st order PDEs in the form
\begin{equation}
a_0\partial_t u + a_1\partial_x u + a_2\partial_y u=0
\label{eq-1}
\end{equation}
then characteristics of the equation (\ref{eq-1}) are integral lines of the vector field $(a_0,a_1,a_2)$ i.e. curves
\begin{equation}
\frac{dt}{a_0}=\frac{dx}{a_1}=\frac{dy}{a_2}.
\label{eq-2}
\end{equation}
There could be just two variables $(t,x)$ or more ... and coefficients are not necessary constant. Yes, for (\ref{eq-1}) characteristics are lines along which $u$ is constant.

But we preserve the same definition of characteristics as integral lines for more general equation f.e.
\begin{equation}
a_0\partial_t u + a_1\partial_x u + a_2\partial_y u =f (t,x,y,u)
\label{eq-3}
\end{equation}
and here $u$ is no more constant along characteristics but solves ODE
\begin{equation}
\frac{dt}{a_0}=\frac{dx}{a_1}=\frac{dy}{a_2}=\frac{du}{f}.
\label{eq-4}
\end{equation}
Further, notion of characteristics generalizes to higher order equations. Definition curves along which solution is constant goes to the garbage bin almost immediately.


2458
APM346 Misc / Re: about the MathJex
« on: September 21, 2012, 03:09:09 PM »
Hi,
I have problem of using the mathjex in my computer, could anyone help me out for this?

First, it is MathJax as it is related to Ajax http://en.wikipedia.org/wiki/Ajax_(programming)

Do you have troubles seeing math? Or there is a raw code? In the latter case see
http://www.math.toronto.edu/courses/apm346h1/20129/about_mathjax.html

Or do you have problems writing math?



2459
Like helping other students to answer questions? Thanks


Yes, the credits will be given for helping.

However JT cannot get any credits as according to BlackBoard there is no such student in the class. Sure, I can try to restore your real name through email—but why should I? (Please, change your screen name to reflect your BlackBoard name).

Finally, do not post in the wrong boards (note the board description; I moved your post)

HTH

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