Brilliant timing! I was studying this and struggling on branch points and branch cuts for most of today.... and you happen to release this video at this very moment :O
@FacultyofKhan
4 жыл бұрын
Hope it helped you!
@captainkielbasa5471
4 жыл бұрын
Excellent! Thank you for honoring requests. My complex var. professor is ~70 and flies through notes without taking a moment to provide a wider perspective of concepts. Thank you so much for all of your series!
@WorldOf173
4 жыл бұрын
I'm just here to support the grind. Hope you're doing well bro!!
@FacultyofKhan
4 жыл бұрын
Thanks so much man! It's easy for me to say during these crazy times but stay healthy and take care bro!
@WorldOf173
4 жыл бұрын
@@FacultyofKhan don't mention it jani! Much love to you and your family 🙏🏼🙏🏼
@xyzct
4 жыл бұрын
What's interesting about complex analysis is that when one studies it for fun -- outside of the pressures of school -- it is actually quite simple. (Well, maybe simple isn't the right term, but you know what I mean.)
@darkseid856
4 жыл бұрын
That's exactly what I am doing right now . But I am also learning multivariable calculus from Khan academy . It is indeed fun . :)
@odineinmann5299
4 жыл бұрын
Everything in maths is easy until you have to start answering questions that arnt just about blind computation. I can tell you certain questions on brack cuts and points are far from 'simple'
@MicroageHD
4 жыл бұрын
It's not so much fun anymore if you have to do 5 classes simultaneously with homework and tight deadlines, tho.
@xyzct
4 жыл бұрын
@@darkseid856, make sure you check out 3Blue1Browns superb channel His graphic-intense lectures on calculus, partial differential equations, linear algebra, and complex numbers are A+++.
@francescagnuva9339
4 жыл бұрын
@@MicroageHD crying this is so true
@trisharoy5756
4 жыл бұрын
You are awesome dude. I was struggling with this
@lorrainerosello4434
3 жыл бұрын
I'm studying for an exam in my Math Methods in Physics class and this really helped! (The textbook only really had about a paragraph on this :/) Thank you!!!
@esisimp123456
4 жыл бұрын
At 1:26 you say we equate the real and imaginary part of both sides and then equate e^u with r and e^{iv} with e^{i\theta} but these are not the real and imaginary parts. Wouldn't the correct thing to do be use Euler formula first and equate e^{u}cos(v) = r.cos(\theta) and same for the imaginary. This might appear pedantic with both approaches leading to the same result but isn't that but isn't this the correct statement ?
@Woodra_YT
3 жыл бұрын
Thank you for clarifying why the end points alpha and alpha + 2pi were not included as part of the branch cuts. Great video^_^
@tokkia1384
Жыл бұрын
I love how you call ln “lawn” 😂
@dwightd3659
3 жыл бұрын
Your interval for theta should be clopen
@ksmg-y1s
Ай бұрын
Absolutely amazing! anything similar about the complex root function?
@sudeshnasahoo6268
2 жыл бұрын
It's a survivor vdo
@soheilabagherilimaei5496
3 жыл бұрын
This is for learning or racing???? The speed is too fast like 2x especially in this difficult concept!
@mihajlovucic8037
3 жыл бұрын
Here so you dont have to replay it 10 times: "The branch that we end up with after the branch cut is not defined on the branch cut"
@soundslikemath860
3 жыл бұрын
First, thank you so much these are great! Second, I think multiple valued functions are still functions, except we have subtly changed the codomain to the powerset of what we thought it was.
@mingmiao364
Жыл бұрын
To recapitulate, 6:55, a branch cut is a portion of a line or curve use to define a region on which a multi-valued function becomes single valued. 7:24 The ways to define a branch cut isn't unique. The common point of all branch cuts is called a branch point. After a branch cut is defined, the function is undefined on the branch cut.
@charliebrett7510
3 жыл бұрын
What is “n”in this video? E.g 2Pi n? Please explain, thank you! If n can be any integer then why is i(theta +2 pi n) different to i(alpha+2pi)? What does this n do??
@LK-cl6jj
3 жыл бұрын
Here is one thing that I am not understanding: If I define Arg(z) to be all angles in ]-pi, pi]. How is Log(z) = ln(z) + i*Arg(z) "deleting" the negative real axis if -pi is included in the interval for the angles ? How is this function still continuous?
@valodkreslobochi7719
4 жыл бұрын
I understand all the things
@Yoyimbo01
4 жыл бұрын
Isn't that branch cut a set of measure zero in the 2D plane? So it shouldn't matter whether we integrate over it or not, if we consider the logarithm as a measurable function? (not sure which measure space is appropriate tho so there might lie the problem somehow)
@jy_decipherer_5515
3 жыл бұрын
Why can’t we define a value on the branch, i.e. set the range of Θ to [α, α + 2π)?
@Physics_mania_supriya
3 жыл бұрын
Hi, nice presentation. I can grasp the idea much easier with the help of this video. By the way, could you please tell me which software you are using to write this black board type learning.
@omanshsharma6796
Жыл бұрын
you have a gorgeous handwriting!! thanks for the explanation!!
@wearytrader535
4 жыл бұрын
Should re-title to "branch cuts for ln"
@FacultyofKhan
4 жыл бұрын
Fair point, but you can argue that complex functions with fractional powers of z can be re-written in terms of the natural log, so the technique discussed here is somewhat generalizable.
@shihaowang3438
3 жыл бұрын
AWESOMEEEE You save my life in the course Asymptotic Analysis.
@ian731
3 жыл бұрын
Why a semi circle(i do now how choose the contour send me a help please.
@ShouEnLin
2 жыл бұрын
thank you for making this helpful video!
@somyakumar3211
3 жыл бұрын
Great video! Despite being a bit fast paced, it was very lucid
@subhamdas6699
4 жыл бұрын
how did I start understanding concept so faster???....
@ebtisammuddatherhassoun
Жыл бұрын
Maaaaaany thanks
@ryanmckenna2047
2 жыл бұрын
That was incredible, thank you.
@alijoueizadeh2896
Жыл бұрын
Thank you.
@ShivamKumar-tg3vp
5 ай бұрын
Beautiful explanation. Thanks a lot
@MissMaglovesmusic
3 жыл бұрын
is there a difference between cut plane and branch cut?
@soohoonc
2 жыл бұрын
Thank you for the visualization, this makes so much more sense now.
@davide816
8 ай бұрын
awesome
@rutwikmore7462
2 жыл бұрын
Nice
@jaredprice7154
4 жыл бұрын
You’re amazing man. Would love to see a video on integrating a multivalued function over the dogbone(dumbbell) contour next.
@debankurbasak3562
3 жыл бұрын
Which app do you use to write?
@motiversity7429
4 жыл бұрын
You're a grt teacher....thanks for these lectures...God bless!!❤
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