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### Messages - Victor Ivrii

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1
##### Chapter 2 / Re: Transport Equation Derivation
« on: January 19, 2022, 05:06:34 AM »
It would be really helpfull if you explained where you took this from (if online TextBook--then section and equation number, if lecture then which lecture and which part).

2
##### Chapter 2 / Re: Week 2 Lec 1 (Chapter 2) question
« on: January 17, 2022, 07:48:38 PM »
Now it is correct $x=Ce^{t}$ and then $C=?$

3
##### Chapter 1 / Re: chapter 1 Problem 4 (1)
« on: January 17, 2022, 01:29:44 AM »
Display formulae are surrounded by double dollars and no empty lines. Multiline formulae use special environments (google LaTeX gather align

4
##### Chapter 1 / Re: home assignment1 Q3(1),(2)
« on: January 16, 2022, 05:47:56 PM »
OK. Remarks:

1. Do not use $*$ as a multiplication sign!
2. Do not use LaTeX for italic text (use markdown of the forum--button I)
3. Escape ln, cos, .... : \ln (x) to produce $\ln (x)$ and so on

5
##### Chapter 1 / Re: Classification of PDEs
« on: January 14, 2022, 01:47:15 PM »
Yes, all linear are also semilinear and all semilinear are also quasilinear. For full mark you need to provide the most precise classification. So, if equation is linear you say "linear", if it is semilinear but not  linear you say "semilinear but not  linear" and so on,... "quasilinear but not  semilinear" and "non-linear and not quasilinear".

6
##### Chapter 1 / Re: Classification of PDEs
« on: January 14, 2022, 02:45:57 AM »
In particular, the definition of a linear PDE, from the textbook, is: $au_{x}+bu_{y}+cu-f=0$, where $f= f(x,y)$. However, if we simply move the the $cu$ to the right-hand side, we get: $au_{x}+bu_{y}=f-cu$. Now, define $g(x,y,u) = f(x,y)-cu$, then $au_{x}+bu_{y}=g(x,y,u)$, and the right-hand side now depends on lower-order derivatives, so by definition, it's quasi-linear. Could someone help identify the issue with this argument?
First, it will be not just quasilinear, but also  semilinear. Second, it will also be linear since you can move $c(x,y)u$ to the left

Good job, you mastered some $\LaTeX$ basics.

7
##### Chapter 1 / Re: Second Order canonical Form
« on: January 13, 2022, 07:24:23 PM »

15
##### Test 1 / Re: Abel's Theorem
« on: October 15, 2020, 08:11:23 AM »
Of some fundamental set (remember a constant factor!)

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