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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
MAT244––Home Assignments / Re: Question Regarding Homework Assignment 2.1 #30
« on: January 14, 2018, 01:26:18 PM »
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
MAT244––Home Assignments / Re: Question Regarding Homework Assignment 2.1 #30
« on: January 14, 2018, 01:06:34 PM »
What should be $c$ in order to $y(t)$ be bounded as $t\to +\infty$? In this case $y(0)=?$

22
MAT244––Home Assignments / MOVED: Assigned Exercises on the webpage
« on: January 13, 2018, 06:30:36 PM »

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
MAT244--Misc / Re: Will partial or complete solutions be posted for homework assignments?
« on: January 13, 2018, 12:17:24 AM »
1) If one of the students posts solution, then yes.

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

25
MAT244––Home Assignments / MOVED: Will partial or complete solutions be posted for homework assignments?
« on: January 13, 2018, 12:15:24 AM »

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
« 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)

28
APM346--Lectures / Re: Classification of PDEs (Chapter Problems 1) clarification
« on: January 12, 2018, 05:01:16 PM »
Please, do use MathJax which is supported and is far superior to html in displaying mathematical snippets.

29
« 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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