### 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.

### Messages - Victor Ivrii

Pages: [1] 2 3 ... 153
1
##### Chapter 1 / Re: chapter 1 Problem 4 (1)
« on: Today at 01:29:44 AM »
Display formulae are surrounded by double dollars and no empty lines. Multiline formulae use special environments (google LaTeX gather align

2
##### 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

3
##### 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".

4
##### 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.

5
##### Chapter 1 / Re: Second Order canonical Form
« on: January 13, 2022, 07:24:23 PM »

15
##### Chapter 7 / Re: Drawing phase portrait with complex eigenvalues question
« on: December 01, 2020, 08:46:13 PM »
"How ellipses wouls look like" means the directions and relative size of their semi-axis. See frame 4 of MAT244_W8L3 handout

Pages: [1] 2 3 ... 153