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Messages - Victor Ivrii

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Home Assignment 2 / Re: Assignment 2.2 Problem3 (16)
« on: January 24, 2019, 11:43:29 AM »
Given the question $u_t + 3u_x -2u_y = xyu$. My steps are:
$$\frac{dt}{1} = \frac{dx}{3} = \frac{dy}{-2} = \frac{du}{xyu} \Rightarrow x=C_1+3t, y=C_2-2t$$
$$xydt = \frac{du}{u} \Rightarrow (C_1+3t)(C_2-2t)dt = \frac{du}{u}$$
$$\ln u = C_1C_2 t + \frac{t^2}{2} (3C_2 - 2C_1) - 2t^3 +\phi(C_1, C_2)$$
Since $C_1=x-3t$, $C_2=y+2t$ we plug
u= f(x-3t, y+2t) \exp \bigl( (x-3t)(y+2t)t +\frac{t^2}{2}(3y+6t-2x+6t) -2t^3\bigr)
with an arbitrary function $f.,.)$ of two variables ($f=e^\phi$).

Home Assignment 2 / Re: Assignment 2.2 Problem3 (16)
« on: January 24, 2019, 06:16:36 AM »
What you really need to do is to replace $C_1,C_2$ by their expression through $x,y,t$

Home Assignment 2 / Re: Home Assignment 2 Problem 2(a)
« on: January 23, 2019, 08:31:16 PM »
Please all these lines tend to $(0,0)$ in one as $s\to -\infty$ ($\frac{dx}{ds}=x$, $\frac{dy}{ds}=y$) but never reach it. Please read again ODE, Chapter 7.

Home Assignment 2 / Re: Concept: Where does the (-) come from
« on: January 23, 2019, 07:10:24 AM »
Yes, I do mean that equation. When I try it myself however, (lines 2 to 3 of my initial post) the math comes out that dx = -tdt.
You need to read Section 2.1 of textbook to understand that equation $au_t+bu_x=f$ requires equation of integral curves $\frac{dt}{a}=\frac{dx}{b}=\frac{du}{f}$. What is on your post are incomprehensibly  written senseless manipulations.

Home Assignment 2 / Re: Concept: Where does the (-) come from
« on: January 22, 2019, 04:49:49 PM »
Do you mean $u_t + tu_x=0$? Then $\frac{dt}{1} = \frac{dx}{t}=\frac{du}{0}$. The first equation implies $$dx=tdt \implies x=\frac{1}{2}t^2+C\implies x-\frac{1}{2}t^2=C.$$

Home Assignment 2 / Re: problem 5 (23)
« on: January 20, 2019, 12:32:48 PM »
I obtain solutions for all 4 subproblems, except two of them with arbitrary function.
No, your solution is incorrect because it is not a continuous single-valued function. I gave you a hint: what is the natural parameter along integral curves?

Home Assignment 2 / Re: problem 5 (23)
« on: January 20, 2019, 04:47:13 AM »
Sure, $x$ and $y$ are not independent along integral curves. To proceed you need to parametrize the integral curve. Think: what is the best way to parametrize it?

Home Assignment 2 / Re: problem4 (20)
« on: January 19, 2019, 07:03:34 AM »
Please learn how to post math properly  Also, asking for help, copy the problem.

Home Assignment 2 / Re: Home Assignment 2 Problem 2(a)
« on: January 18, 2019, 09:31:56 PM »
Since integral curves are rays (straight half-lines) from $(0,0)$  the solution in the plane wit the punched out origin is any function, constant along these rays, in particular $u=f(y/x)$.

But if we want solution in the whole plane, $u$ must be continuous at $(0,0)$ and since all rays intersect there $u$ is just a constant.

Home Assignment 2 / Re: Secondary Textbook Chp1.2 Exercise 10
« on: January 18, 2019, 09:05:21 PM »
Read Section 2.1, Subsection  "semilinear equations"

Home Assignment 1 / Re: Home Assignment 1
« on: January 16, 2019, 04:57:59 PM »
Junjing, you are right but I am not sure if anyone but me would be able to read your solution

Home Assignment 2 / Re: Home Assignment 2 problem 1(a)
« on: January 15, 2019, 05:04:28 PM »
You draw just a bit more than one period and say "$\pi$-periodic"

APM346--Misc / Re: physical interpretation
« on: January 15, 2019, 05:02:51 PM »
Physical interpretation is useful. However Quizzes, Tests and Exam neither test nor require any knowledge of Physics. Like in ODE or Calculus I, II classes.

APM346--Misc / Welcome to APM346
« on: January 07, 2019, 06:30:22 AM »
Welcome to this forum!

The main purpose of this forum is not the communication with instructors but peer-to-peer. I noticed that some of you answer the questions of your peers and I really appreciate, but I would like to see more -- much more -- of this!

It runs as aid to the class website. More permanent and systematic information is placed on website, while forum is for discussion. Please read before registering!

  • You can select any username (login) you want (take a rather short one). Username is what only you (and Admin) can see.
  • However  change your (screen) Name  (the one which everybody sees) to one easily identifiable (Admin should be able to identify you with a student enrolled to this course--and matching BlackBoard name; otherwise your posting privileges could be reduced or revoked):  Open Profile > Account Settings and look for "Name".
  • It would be preferable to use your University of Toronto email address.
  • BTW you can have a cool avatar too. Please do not display any confidential info.
  • You cannot change the loginname (used for login).  But there is no need.  Nobody except you knows your password - even Admins - but Admins don't need  to know it.

Some forum rules
  • Please use different boards according to their description (I will create new ones if needed).
  • Do not hijack topics: if a topic is devoted to some question, do not post anything which is not related. Start a new topic.
  • On the other hand, do not start new topic answering to the existing post; use the same topic.
  • Do not put in the same post several not related things - make several posts instead (in different topics).
  • Do not post solution which coincides with the solution already posted by someone else; exception: typed solution beats the scanned one.
  • Do not spam (post irrelevant messages, especially to promote something), flood (post many messages with very little or no sense, like "me too", "I like this post", ...) or flame (messages, containing personal attacks and heated arguments).
  • Do not thank instructors.
  • Do not post snapshots of paper documents, scan them (with the scanner or smartphone).
  • Do not use red color (it belongs to Admins and Moderators), large fonts
  • Read and search before postings.
  • Use common sense.

  • This semester karma does not translates into Bonus mark points (there are plenty reasons for this) 
  • On the other hand, your posts and active participation in the class will be a decisive factor if you ask me for a recommendation letter for a Graduate School. To write such letter I need to know something about you beyond your marks (and your final mark is in the transcript anyway). Participation in the forum automatically leaves a trace.

Have questions?
  • If you have a question which you think is of general interest--ask it on the Forum rather than via email.

  • Both this forum and website use MathJax to display mathematics.

MAT244--Misc / Re: Quiz 5 explanation (was Unfair quiz)
« on: December 21, 2018, 05:30:52 PM »
For those who had < 4 for this Quiz Quiz mark was based on the best 4.5 quizzes (which means that the 5-th best had a half weight).

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