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### Messages - Victor Ivrii

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16
##### Chapter 2 / Re: Text Book 2.4 Example 2.1
« on: February 20, 2022, 10:04:48 AM »
We integrate from $t=0$ because for $t=0$ initial conditions are done. $-1<t$ is a domain where $f(x,t)$ is defined

17
##### Chapter 2 / Re: Derivation of D' Alembert formula under Characteristic Coordinate
« on: February 20, 2022, 10:01:28 AM »
Reproduce formula correctly (there are several errors) and think about explanation why $\phi'(\xi)=0$.

18
##### Quiz 3 / Re: LEC0101 Quiz3-1c
« on: February 15, 2022, 12:46:54 PM »
It is the same answer for $x>ct$ and $x-ct$. Explain why

19
##### 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

20
##### Chapter 3 / MOVED: Chapter 4.2, Example 6
« on: February 14, 2022, 07:10:42 AM »

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

22
##### Chapter 3 / Re: Homework Assignment Week5
« on: February 06, 2022, 01:53:33 PM »
Thanks! Fixed online TB

23
##### Chapter 3 / Re: Chapter 3.2 Problem 9
« on: February 06, 2022, 01:25:46 PM »
You almost there. Think!

24
##### 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

25
##### Chapter 3 / MOVED: S2.2 Q1
« on: February 02, 2022, 06:22:00 PM »

26
##### 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.

27
##### 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)

28
##### Chapter 2 / Re: Online textbook, Chapter 2.6, example 7
« on: February 01, 2022, 05:56:58 AM »
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 $\{x=-t, t>0\}$.

29
##### 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

30
##### 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.

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