### Recent Posts

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91
##### Chapter 1 / Question about the posted solution for HW1 3c
« Last post by Yuanhan (Phyllis) Peng on January 27, 2022, 12:39:22 PM »
I am confused about why when we integrate the left hand side Ux/e^u, we used the x' in Ux(x', y) expression, but we didn't change x in e^u(x,y)

The screenshot is attached.

92
##### Chapter 2 / Re: Chapter 2.2 problem 2
« Last post by Zicheng Ding on January 27, 2022, 08:19:58 AM »
$x^2 - y^2 = C$ is a hyperbolic curve so it has two parts for x. I see now, thank you professor.
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##### Chapter 2 / Re: Chapter 2.2 problem 2
« Last post by Victor Ivrii on January 27, 2022, 08:04:10 AM »
Both signs. What are curves $x^2-y^2=C$?
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##### Chapter 2 / Chapter 2.2 problem 2
« Last post by Zicheng Ding on January 26, 2022, 09:22:59 PM »
Chapter 2.2 problem 2 equation (9): $u_t + yu_x + xu_y = x$
and we get $\frac{dt}{1} = \frac{dx}{y} = \frac{dy}{x} = \frac{du}{x}$
By solving $\frac{dx}{y} = \frac{dy}{x}$ first we get $C = x^2 - y^2$
But we solving for either $\frac{dt}{1} = \frac{dx}{y}$ or $\frac{dt}{1} = \frac{dy}{x}$ we need to substitute $x$ for $y$ or the other direction, so in this case we will have a square root function like $x = \pm \sqrt{y^2 + C}$
I am not entirely sure whether or not we should proceed with the $\pm$ sign here or is there another easier approach to this question?
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##### Quiz 1 / Re: Second Order PDE Classification on Quiz 1?
« Last post by Victor Ivrii on January 24, 2022, 05:48:42 AM »
Please post non-mathematical questions in Quercus discussions.
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##### Chapter 2 / Re: Transport Equation Derivation
« Last post by Victor Ivrii on January 24, 2022, 05:46:09 AM »
Then your best shot would be
• either to ask during Prof Kennedy's Office hours
• or to formulate the problem and define everything  (that is $u, v, S, \tilde{S}$) here by yourself without screenshots
My guess that it is a continuity condition.
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##### Quiz 1 / Second Order PDE Classification on Quiz 1?
« Last post by Yifei Hu on January 23, 2022, 10:31:07 PM »
Hi professor, in homework 1, classification problem does not touch upon second order PDE classifications such as elliptic, parabolic and hyperbolic. Will these be tested on Quiz 1?
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##### Chapter 2 / Re: Transport Equation Derivation
« Last post by Yifei Hu on January 23, 2022, 10:17:29 PM »
Hi Professor Ivrii, this comes from Christopher's lecture #3 when he discussed transport equation, directly from his lecture notes #3 on top of page 2 : )
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##### Chapter 1 / HW1-Problem2
« Last post by Yifei Hu on January 20, 2022, 01:33:08 PM »
Can anyone help me check the answer? Thanks

(11) Second order, linear, homogeneous
(12) Second order, quasilinear
(13) Third order, linear, homogeneous
(14) Third order, quasi linear
(15) Forth order, linear homogeneous
(16) Forth order, linear homogeneous
(17) Forth order, linear inhomogeneous
(18) Forth order, general non-linear

Can we say that, to classify whether an equation is linear, we don't need to move the L.O.T to right hand side, but when classifying non-linear equations , we need to do so?
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##### Chapter 1 / HW1-Problem 1
« Last post by Yifei Hu on January 20, 2022, 01:17:24 PM »
Can anyone help me check the answer? Thanks

(1) linear-homogeneous
(2) Quasi-linear
(3) Semi-linear
(4)Quasi-linear
(5) Semi-linear
(6)Quasi-linear
(7)Quasi-linear
( Semi-linear
(9)Quasi-linear
(10) Quasi-linear
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