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61
Chapter 3 / C3.2/P4/Q10
« Last post by yingxuanwang on February 16, 2022, 09:32:47 PM »
Hi I have facing difficulty with solving the 10th part of the Problem 4 in Chapter 3.2

This equation is quite different from others in Problem 4, since I am really not sure with my solution, can anyone check for me? My friend said he will solve it in a different way and he thinks my solution is wrong but he did not actually solve it. I have attached the question and my solution. It is really near the quiz and I have struggled on this problem for two days, please help me! :( :( :(
62
Chapter 4 / C3.2/P4/Q10
« Last post by yingxuanwang on February 16, 2022, 09:29:58 PM »
Hi I have facing difficulty with solving the 10th part of the Problem 4 in Chapter 3.2

This equation is quite different from others in Problem 4, since I am really not sure with my solution, can anyone check for me? My friend said he will solve it in a different way and he thinks my solution is wrong but he did not actually solve it. I have attached the question and my solution. It is really near the quiz and I have struggled on this problem for two days, please help me! :( :( :(
63
Quiz 3 / Re: LEC0101 Quiz3-1c
« Last post by Victor Ivrii on February 15, 2022, 12:46:54 PM »
It is the same answer for $x>ct$ and $x-ct$. Explain why
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Quiz 1 / LEC0101 Quiz1-1a
« Last post by Yukun Zhang on February 14, 2022, 08:06:10 PM »
Here is my answer of Quiz1-1a
65
Quiz 3 / Quiz3 1-F
« Last post by Kexin Wang on February 14, 2022, 07:08:03 PM »
\begin{equation}
    \begin{cases}
      u_{tt}- c^2u_{xx} = 0 &\ x>0\\
      u\rvert_{t = 0} = sech(x) &\ x>0\\
      u_{t}\rvert_{t = 0} = 0 &\ x>0\\
      u_{x}\rvert_{x = 0} = 0 &\ t>0\\
    \end{cases}       
\end{equation}

For this problem, my approach was to extend $sech(x)$ as an even function for $x \in R$. Since $sech(x)$ is already an even function so we can write the set of equations as follows.

\begin{equation}
    \begin{cases}
      u_{tt}- c^2u_{xx} = 0 &\ x>0\\
      u\rvert_{t = 0} = sech(x)\\
      u_{t}\rvert_{t = 0} = 0 &\ x>0\\
    \end{cases}       
\end{equation}

And by using D'Alembert Formula $u(x,t) =\frac{1}{2}[g(x+ct)+g(x-ct)] $ we can simplify it as $\frac{1}{2}[sech(x+ct)+sech(x-ct)]$ $,x>0$
66
Quiz 3 / LEC0101 Quiz3-1c
« Last post by Yukun Zhang on February 14, 2022, 04:55:54 PM »
Here is my answer for Quiz3-1c
67
Chapter 4 / Re: Chapter 4.2, Example 6
« Last post by Victor Ivrii 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
68
Chapter 3 / MOVED: Chapter 4.2, Example 6
« Last post by Victor Ivrii 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
69
Chapter 4 / Chapter 4.2, Example 6
« Last post by Zicheng Ding on February 13, 2022, 01:14:16 PM »
In chapter 4.2, example 6, I was a little confused about the notation. My understanding is that $\omega_n$ are the roots for equation $\tan(\omega l) = \frac{(\alpha + \beta)\omega}{\omega^2 - \alpha\beta}$, so should the equation for $X_n$ be $X_n = \omega_n \cos(\omega_n x) + \alpha\sin(\omega_n x)$ instead of $X_n = \omega \cos(\omega_n x) + \alpha\sin(\omega_n x)$ (the first $\omega$ change to $\omega_n$)? I attached a screenshot of the example.

Another minor thing that I noticed is that for homework assignment 6/7, it said problems 1-11 for section 4.1 and 4.2, but there are no problem 11 in neither textbook version, so I guess it was a typo on Quercus.
70
Chapter 3 / Re: Chapter 3.2 Problem 9
« Last post by Victor Ivrii on February 06, 2022, 02:21:30 PM »
Indeed. You got it!
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