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Messages - Victor Ivrii

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16
Web Bonus Problems / Re: Web bonus problem -- Week 2
« on: January 15, 2018, 12:32:21 AM »
I'm pretty sure my integration was wrong to begin with - I was confused with the functions' arguments...
If we can't integrate (B), maybe we can differentiate (A)?
Yes, indeed. $\phi '(...)$ is a derivative with respect to ... , not $x$. And if you have ideas try them, rather than waiting my approval..

17
Web Bonus Problems / Re: Web bonus problem -- Week 2
« on: January 14, 2018, 10:42:20 PM »
Ioana
Equation (A), (B) (I put tags here) are correct, but (C) does not follow from (B). Explain why.

Hint. We cannot integrate (B) but .....

18
Web Bonus Problems / Re: Web bonus problem -- Week 2
« on: January 14, 2018, 07:24:10 PM »
Ziyuan
What are $C_1$ and $C_2$ in your "solution"? Please, read Sect 2.3.


Jaisen
D'Alembert formula as you wrote works only in the case with the data at $t=0$ and could be modified for the case with the data at $t=t_0$ (which is constant).

You need to plug this general solution into initial conditions and then find $\phi$ and $\psi$ from there

19
Web Bonus Problems / Re: Web bonus problem -- Week 2
« on: January 14, 2018, 02:00:06 PM »
Hint: What is the general solution of (\ref{A})?

20
Please look how I modified your post. This is how mathematics should be typed. Also it is not important that $e^t$ is increasing but that it is unbounded as $t\to \infty$.

21
What should be $c$ in order to $y(t)$ be bounded as $t\to +\infty$? In this case $y(0)=?$

23
MAT244--Misc / Re: Assigned Exercises on the webpage
« on: January 13, 2018, 06:30:18 PM »
Good catch. Corrected on that page

If it says "In problems from 21 to 35" but only 23, 24, 31 are here, you solve only 23, 24, 31

24
1) If one of the students posts solution, then yes.

2) General (non-mathematical) questions should be posted in this board.

26
Web Bonus Problems / Re: Web bonus problem -- Week 2
« on: January 12, 2018, 08:33:40 PM »
Jaisen: definitely does not satisfy even equation.

Sheng: satisfies equation but not conditions (I checked solution against old conditions).

I made an error. Please ignore old initial conditions. You need to post calculations, not just answers.

27
MAT244--Announcements / Weekly updates
« on: January 12, 2018, 05:04:59 PM »
1) Posted home assignments and handouts for Week 3
http://www.math.toronto.edu/courses/mat244h1/20181/homeassignments.html
(reload page if Week 3 is not displayed)

2) Added poll to topic About textbook



28
Please, do use MathJax which is supported and is far superior to html in displaying mathematical snippets.

29
APM346--Announcements / Weekly updates
« on: January 12, 2018, 09:07:40 AM »
1. Updated (extended) Subsection 2.1.6 Quasilinear equations

2. Posted Web bonus problem--Week 2

3. Bonuses for Weeks 1--2 not posted yet.

30
Web Bonus Problems / Web bonus problem -- Week 2
« on: January 12, 2018, 09:03:13 AM »
Find solution $u=u(x,t)$ and describe domain, where it is uniquely defined
\begin{align}
&u_{tt}-u_{xx}=0,
\label{A}\\[2pt]
&u|_{t=x^2/2}= x^3,
\label{B}\\[2pt]
&u_t|_{t=x^2/2}= {\color{blue}{2}}x.
\label{C}
\end{align}
Correction: I replace $x$ by $2x$ in (\ref{C})

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