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### Messages - Victor Ivrii

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46
##### Chapter 3 / Re: Rouché's Theorem
« on: December 12, 2020, 06:25:05 PM »
You need to indicate that there are no zeroes on $\gamma$

47
##### 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

48
##### Chapter 4 / Re: Section 4.4 Past Final Exam Question
« on: November 22, 2020, 05:19:33 AM »
There could be misprints

49
##### Chapter 4 / Re: General Question related to something in Section 4.1
« on: November 13, 2020, 12:54:44 PM »
For higher order equations it is covered in MAT244-LEC0201-W6L2 (see modules). It is mandatory material.

50
##### Chapter 4 / Re: 4.2 question 28
« on: October 25, 2020, 01:13:50 PM »
you need to write it, if you hope for any answer

51
##### Test 1 / Re: 2020TT1 Deferred Sitting #1
« on: October 15, 2020, 08:17:16 AM »
Indeed, instead of $\log(\pm w)$ with $+2\pi mi$ we write $\log(w)$  with $+\pi mi$ since $\log (-w)=\log(w)+\i i$

52
##### Test 1 / Re: Abel's Theorem
« on: October 15, 2020, 08:11:23 AM »
Of some fundamental set (remember a constant factor!)

53
##### Chapter 2 / Re: Section 2.2 "closed form" Qs
« on: October 13, 2020, 09:35:57 AM »
Yes, some of them are geometric series, and some of $e^{z}$, $\sin(z)$, $\sinh(z)$ and so on. However some can be derived from those, ether by substitution (f.e. $z^2$ instead of $z$), some by integration, differentiation, multiplication by $z^m$ or combination of both. F.e. consider geometric $\dfrac{1}{1-z}$. Integratinfg we can get power series for $-\Log (1-z)$, diffeerentiating for $\frac{1}{(1-z)^m}$ ,...

54
##### Chapter 1 / Re: Section 1.4: Question 29 Proof Check
« on: October 08, 2020, 09:27:59 AM »
Indeed

55
##### Chapter 2 / Re: Problem of Section 2.6 Q28
« on: October 03, 2020, 07:54:48 AM »
Hi there, I think there might be some problem with Q28. After I found the integrating factor and then solve for the solution, it's impossible to find the solution of my h(y) in this case (see the last line of my writing).
If you found an integrating factor correctly there should be no problem to $h(y)$. There is a problem with your solution, not with the problem.
In the textbook, it is e^(-2y). Maybe this one is correct.
Both are correct

56
##### Chapter 2 / Re: Question on 2.1 Example 10
« on: October 03, 2020, 04:50:32 AM »
is du/dx+i dv/dx? Why can't we take the derivative with respect to y?
You can take also derivative by $y$ but you need to multiply it by $i$ (think why)

57
##### Chapter 1 / Re: How to solve the question on section 1.4 of the text book Page42
« on: October 03, 2020, 04:47:21 AM »
Try to solve it by yourself (it follows right from the definition)

58
##### Chapter 1 / Re: why complex plane closed
« on: October 03, 2020, 04:46:26 AM »
why the complex plane is both open and closed? why did it close? Because by definition, a set is called closed if it contains its boundary. And I don't see the complex plane contains its boundary.
And what is the boundary of $\mathbb{C}$?

59
##### Chapter 1 / Re: Section 1.4: Question 29 Proof Check
« on: October 03, 2020, 04:45:02 AM »
You should remember that each segment of the polygonal curve may be served not by two discs, but several discs (think why)

60
##### Chapter 1 / Re: What is the meaning of complex number
« on: October 03, 2020, 04:42:37 AM »