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
Show Posts
This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.
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
Please post in the appropriate subforum
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
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.