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Quiz-3 / QUIZ3 5301 TWO-C
« Last post by Jin Qin on February 19, 2021, 06:30:49 PM »
Hi, this is my answer for QUIZ3 TWO-C in section 5301. Hope this can help you out!
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Chapter 3 / Re: 3.1 Heaviside step function
« Last post by Victor Ivrii on February 09, 2021, 05:11:06 AM »
Everything is correct. You need to look carefully at limits in the integrals
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Chapter 3 / Re: 3.2 Theorem1
« Last post by Victor Ivrii on February 09, 2021, 05:10:26 AM »
$\int_0^\infty$. I fixed it
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Chapter 3 / 3.2 Theorem1
« Last post by SelinaW on February 09, 2021, 04:05:58 AM »
I am not sure what should this integral integrate over. Is it -∞ to +∞ or 0 to +∞?
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Chapter 3 / 3.1 Heaviside step function
« Last post by SelinaW on February 09, 2021, 04:00:59 AM »
I believe as t->0+ and x>0, the integral I marked in red should be sqrt(pi), then U(x, t) should be 1/2. I do not know how we get 1.
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Chapter 2 / Re: Example 6 from Week 3 Lec 2
« Last post by Victor Ivrii on February 02, 2021, 04:31:46 PM »
Indeed
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Chapter 2 / Example 6 from Week 3 Lec 2
« Last post by SelinaW on February 02, 2021, 10:22:27 AM »
Should here be -2 instead of -25?
I have attached the picture below.
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Quiz 1 / Re: Quiz 1 - Variant 2E - Problem 2
« Last post by Victor Ivrii on January 29, 2021, 11:45:32 AM »
Try to avoid high-riser notations. Several years ago I was a referee for a paper which used notations like this $\widehat{\dot{\widetilde{\mathcal{D}}}}$ and sometimes this little pesky dot was missing  :D
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Quiz 1 / Re: Quiz 1 - Variant 2E - Problem 1
« Last post by Victor Ivrii on January 29, 2021, 11:41:45 AM »
Indeed, this equation has $u=0$ as a solution but the notion of "homogeneou"s does not apply to nonlinear.
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Quiz 1 / Quiz 1 - Variant 2E - Problem 2
« Last post by Gavrilo Milanov Dzombeta on January 29, 2021, 10:55:56 AM »
$$\text{Find the general solutions to the following equation: }
u_{xxy}=x\cos(y)$$
\begin{gathered}
\nonumber
u_{xxy}=x\cos(y)\\
u_{xx}=x\sin(y) + f(x)\\
u_{x}=\frac{x^2}2\sin(y) + \tilde{f}(x) + h(y) ;\tilde{f}_x=f \\
u= \frac{x^3}6\sin(y) + \tilde{\tilde{f}}(x) + xh(y) + g(y);\tilde{\tilde{f}}_{xx}=f \\ 
\therefore u(x,y)=\frac{x^3}6\sin(y) + \tilde{\tilde{f}}(x) + xh(y) + g(y).\\
\text{Where $f(x),h(y),g(y)$ are arbitrary functions, and $\tilde{\tilde{f}}$ is twice differentiable.}
\end{gathered}

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