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Messages - Victor Ivrii

Pages: 1 [2] 3 4 ... 154
16
Chapter 4 / Re: Chapter 4.2, Example 6
« on: February 14, 2022, 07:12:14 AM »
Indeed, fixed. For consistency added index $_n$ to similar places of Example 4.2.7


Please post in the appropriate subforum

17
Chapter 3 / MOVED: Chapter 4.2, Example 6
« on: February 14, 2022, 07:10:42 AM »
This topic has been moved to Chapter 4.

http://forum.math.toronto.edu/index.php?topic=2654.0

18
Chapter 3 / Re: Chapter 3.2 Problem 9
« on: February 06, 2022, 02:21:30 PM »
Indeed. You got it!

19
Chapter 3 / Re: Homework Assignment Week5
« on: February 06, 2022, 01:53:33 PM »
Thanks! Fixed online TB

20
Chapter 3 / Re: Chapter 3.2 Problem 9
« on: February 06, 2022, 01:25:46 PM »
You almost there. Think!

21
Chapter 2 / Re: S2.2 Q1
« on: February 02, 2022, 06:25:02 PM »
  • If you do not know this integral you need to refresh Calcuus I. one of basic integrals. Or have a table of basic integrals handy.
  • Since $x^2+y^2=c^2$ is a circle, you can substitute $x=c\cos(s)$ and $y=c\sin(s)$ and then observe that $s=D-s$. It gives you the answer, less nicely looking than the one you wrote.
  • Expressing $x, y$ through $t,c,d$ you can express $C=c\cos(d)$ and $D=c\sin(d)$ through $x,y,t$ which would give you that nice answer.

Write \cos , \sin , \log .... to produce proper (upright) expressions with proper spacing

22
Chapter 3 / MOVED: S2.2 Q1
« on: February 02, 2022, 06:22:00 PM »
This topic has been moved to Chapter 2.

http://forum.math.toronto.edu/index.php?topic=2649.0

23
Chapter 2 / Re: Ut+xUx=0
« on: February 01, 2022, 12:16:37 PM »
As $x>0$ it is a correct calculation. However $f(xe^{-t})$ re,mains valid for $x<0$ while $f(t-\ln (x))$ does not.

24
Chapter 2 / Re: f(x) in Method of Characteristics
« on: February 01, 2022, 12:12:52 PM »
Yes, there are many answers which are correct because they include arbitrary functions (and in ODE arbitrary constants)

25
Chapter 2 / Re: Online textbook, Chapter 2.6, example 7
« on: February 01, 2022, 05:56:58 AM »
Quote from: Zicheng Ding on January 31, 2022, 09:04:09 PM
For the middle region in red, since $\psi(x - \frac{t}{3})$ is undefined,
It is defined, because on the line $\{x=-t, t>0\}$ we have not 1 but 2 boundary conditions, so in the domain $\{x>-t, t>0\}$ we have essentially a Cauchy problem with the date on the line consisting of two rays: $\{x>0,t=0\}$ and $\{x=-t, t>0\}$.

26
Chapter 1 / Re: HW1 Problem 1 （2）
« on: January 29, 2022, 05:35:01 AM »
You should ask everybody, not just me. And the question was a bit different anyway: to classify an equation

27
Chapter 1 / Re: HW1 Problem 6 （41）
« on: January 28, 2022, 01:41:36 AM »
Yes, it is correct: $u=H(x)+m(y,z)$ where $H$ and $m$ are arbitrary functions.

28
Chapter 1 / Re: Question about the posted solution for HW1 3c
« on: January 27, 2022, 03:59:38 PM »
It was a misprint; it should be $e^{u(x',y)}$ in the denominator

29
Chapter 2 / Re: Chapter 2.2 problem 2
« on: January 27, 2022, 08:04:10 AM »
Both signs. What are curves $x^2-y^2=C$?

30
Quiz 1 / Re: Second Order PDE Classification on Quiz 1?
« on: January 24, 2022, 05:48:42 AM »
Please post non-mathematical questions in Quercus discussions.
Please read description of Quiz 1.

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