You actually didn't forget the "i" at 14:38 but it got erased at 13:28 haha
@shandyverdyo76885 жыл бұрын
@@hiy9846 it's not. It's from C1
@tubhyammehta65985 жыл бұрын
Pi- m
@arnavanand80375 жыл бұрын
Hoowoo!!!!
@sparsetable4 жыл бұрын
Doctor Pi M (Peyam) :0
@CLeonard4845 жыл бұрын
Best explanation of contour integral I have seen. Hopefully, y'all continue with a series of more complex integrals.
@blackpenredpen5 жыл бұрын
The One and Only Peyam has many more videos on his channel. You can check the link in description. This is meant to be a starter. : )
@ガアラ-h3h Жыл бұрын
Essentially I can be treated as a constant becaus it is one
@gsniteesh37945 жыл бұрын
Please make a video on complex analysis :)
@whyit4875 жыл бұрын
Marvel: Infinity War is the most ambitious crossover event! Bprp and Dr. Peyam: Hold my markers
@blackpenredpen5 жыл бұрын
Why It? Hahaha thanks!! And also Chester!
@victorpaesplinio2865 Жыл бұрын
This video summarizes my calc 4 exam for next month on residue theorem. Thank you very much!
@Vampianist35 жыл бұрын
This is the first time I know that a lot of Peyam’s videos were taken in his office. Always liked the picture beside the board.
@Erik207665 жыл бұрын
Complex analysis is *really* cool but for people to understand it from the ground and then people don’t have to assume it’s magic :) Basically the reason why the residue is important can be explained by the Taylor series of the (analytic, meaning it has a complex derivative) function, breaking it up into a sum of different powers of z. Every term has a nice primitive function [remember integral of x^n=(x^(n+1))/(n+1) ] *except* the 1/z term! (What’s kind of interesting in real analysis is really important in complex analysis here.) It’s the derivative of the complex logarithm which is multi valued. If we integrate on a closed curve, are start and endpoint is the same and so those terms with a primitive function integrate to zero! The exception is 1/z and famously the (complex) logarithm increases by 2*pi*i in one lap around the origin. So the only thing we care about when integrating on a closed curve is where the function has any singularities (else the 1/z term coefficient is necessarily 0 as the function is “nice”) and in those singularities, what the coefficient of 1/z is, and we call that the residue! (Note: some singularities have residue 0, like 1/z^2 in z=0, and do not contribute to the integral. It also does not have to be a simple “pole”, you can also integrate e^(1/z) around z=0 for example. This is an essential singularity where the function approaches infinity and 0 in the same point but it does not matter!)
@FractalMannequin5 жыл бұрын
To compute the residue just notice that 1/(z^2+1) = 1/(z-i) * 1/(z+i) and the second factor has no poles at z=i, so its Laurent expansion coincides to its Taylor expansion. The -1-th coefficient of 1/(z^2+1) now must be 1 (i.e., 1/(z-i)'s -1-th coefficient) times the 0-th coefficient of 1/(z+i), which is its value at z=i, namely 1/2i. So the residue is 1/2i (or -i/2).
@egillandersson17805 жыл бұрын
Hokusai's Great Wave and Van Gogh's Starry Night : Peyam is definitely the Artist of mathematics ! Well, about contour integral, I have to work a bit more :-(
@habouzhaboux94885 жыл бұрын
Finally I found a worth watching video about contour integrals
@tobyinsley90105 жыл бұрын
Honestly this is the most intuitive and clear explanation I've found of the process of finding bounds with triangle inequality etc - thanks Dr. Peyam, this was very useful!
@itachi20111005 жыл бұрын
Is it me or is this a lot more interesting than the usual videos? It gives an insight to how you'd work in university.
@kcldnx34852 ай бұрын
I just had complex analysis last semester and saw the thumbnail. I immediately thought residue theorem and it was super fun to see you use it
@atrath5 жыл бұрын
This video brought back some memories from graduate school... I really miss those times...
@blackpenredpen5 жыл бұрын
atrath : )))
@IoT_5 жыл бұрын
Hello ,Dr. πm) I would like to say thank you that you invited blackpenredpen to your lecture because they asked very useful questions for novices. As for me, I was graduated from the engineering faculty of the russian university and surprisingly I had all these stuff with proofs (surprisingly because even mathematicians have less mathematics than us- engineers ). Anyway , thank you that you reminded me of the best subject - Complex Analysis) . By the way ,Residue in Russian means "Вычет" 😁
@RapidScience5 жыл бұрын
Wow this is amazing, he made some amazing points throughout the video
@cbbuntz3 жыл бұрын
Peyam's enthusiasm for math is infectious
@nishan3755 жыл бұрын
Love dr. P. Very approachable person and loves his subject.
@manfredwitzany22335 жыл бұрын
Calcualtion of the residuum is much easier than demonstrated. As the pole is of first order, you can use the following identity for residuum calculation: \textstyle \operatorname {Res}_{a}f=\lim _{{z ightarrow a}}(z-a)f(z) The term (z-a) cancels out and the remaining function value is equal to the residuum. I have integrated some even more complex functions. This method is pretty easy.
@chris-hj2qd2 жыл бұрын
Man, how beautiful is it to see a culture that appreciates learning. So wonderful.
@kwirny5 жыл бұрын
Dr Peyam is genius dude
@GicaKontraglobalismului6 ай бұрын
Nice paintings man .... Van Gogh, Hokusai , and something modernist with many colours resembling the Inca Empire flag ....
@carcaperu40415 жыл бұрын
A question about determined integrals that are equal to pi**N As this video shows Integral of 1/(x^2+1) from -inf to inf= pi ?Is there any function integrated on an interval that is equal to pi**2 or pi**N (where N is an integer N=2, 3.....). Obviously the limit of the integral do not contain explicit pi nor the integrated function. Nor the function contains trigonometric (or inverse of) functions.
@user-wu8yq1rb9t2 жыл бұрын
One of your best videos in all the time, I watched it for several times! Thank you so much dear *bP🖋️rP🖍️*
@bandamkaromi5 жыл бұрын
wow!! Dr. Peyam. Brilliant try. Thank you. BlackPenRedPen!!
@remlatzargonix13295 жыл бұрын
This was cool.....Dr. P. rocks!
@radiotv6245 жыл бұрын
This is so wholesome haha I love complex analysis as well!
@flaviusclaudius75105 жыл бұрын
Nasty flashbacks to undergrad ... while complex analysis is amazing, I found it very challenging.
@douglasstrother65844 жыл бұрын
It's more fun without the exams!
@flaviusclaudius75104 жыл бұрын
@@douglasstrother6584 I should probably dig out my lecture notes, then!
@douglasstrother65844 жыл бұрын
@@flaviusclaudius7510 You'll be surprised by what you *did* understand. It's a lot more fun w/o the time pressure.
@CDChester5 жыл бұрын
Worth every minute
@blackpenredpen5 жыл бұрын
C. D. Chester totallly!!!
@Pete-Prolly5 жыл бұрын
Dr. Peyam is stylin!! Look at the sweet watch!! Steady pimpin' these lil Math tricks! Get Σ playa!! (I don't really talk like this; its just fun and I'm just very enthused about your attire.) But yo shirt be lookin' ill af; is dat silk???
@nimmira5 жыл бұрын
Ohhh ... Dr Peyam is left-handed!!! :D
@erikawanner73555 жыл бұрын
Where was this channel when I was in college?!?! 😊
@CofeeAuLait5 жыл бұрын
MIND BLOWN.
@ProJeT3Toad5 жыл бұрын
Uhh Dr.Peyam rocking the Rolex, okay, I see you xD
@kingbeauregard5 жыл бұрын
You guys are fun. I want to see a Very Special Episode of "The Big Bang Theory" where you give them all swirlies.
@CDChester5 жыл бұрын
i can picture this so vividly
@birupakhyaroychowdhury9745 жыл бұрын
Loved it....!!!!
@lukestanislaus88875 жыл бұрын
Really enjoyed this one!
@PauloYgor15 жыл бұрын
Bprp: because "i" don't like to be on the bottom. Dr. P.: Yes, Nice. Bprp: ... Someone don't watch my videos Hahaha hahaha
@Galileosays5 жыл бұрын
Great to see this again. We used the limit rule. The Laurent series was for me an eye opener, or should I say an i opener.
@elizabethmeghana96144 жыл бұрын
Wooooowwwwwwwwwwwwwwwwwwwww I really appriciate the teacher , well done sir
@3ia18_prasetyaharkrisnowo75 жыл бұрын
Pls can you make a video about macclaurin series thx.
@mtaur41133 жыл бұрын
Sometimes you do something just to see that it agrees with what you already know. Other times you do it because it is actually easier.
@DarioCasarotti5 жыл бұрын
Why didn't you use the evaluation of arctan(x) between inf and -inf? It was much simpler... Did you just want to show an alternative method?
@blackpenredpen5 жыл бұрын
yes
@thfwil5 жыл бұрын
Happy Pride Peyam!!
@drpeyam5 жыл бұрын
Tom FW Happy pride 🙂
@muhammadqasim70565 жыл бұрын
Do the integral of y=x^^x
@angelmendez-rivera3515 жыл бұрын
Muhammad Qasim Dilawari It cannot be done. f(x) = x^^x provided f:R -> R is not integrable, since it is discontinuous almost everywhere. In fact, it is defined almost nowhere.
@muhammadqasim70565 жыл бұрын
Ah shit,my bad
@LouisEmery5 жыл бұрын
I would think that someone who could do 1000 integrals, would be a complex analysis jock.
@lordlix64835 жыл бұрын
Awesome Video 😄
@elizabethaugustin54944 жыл бұрын
I enjoyed math for the first time
@Serghey_832 ай бұрын
Res. Integral [C] dF(z)
@federicopagano65905 жыл бұрын
Excelent video dr peyam. I wonder what would have happened ...if when we were about to integrate 1/(z^2+1) wich goes to zero....instead we had put Arctan(z) what would be the result? Again 0? From z=R+0i to z=-R+0i the integrand satisfies Cauchy Riemann so...why not....
@ThisIsEduardo5 жыл бұрын
Great video !
@rot60155 жыл бұрын
Chester has a great shirt😄
@blackpenredpen5 жыл бұрын
Rot definitely
@carviryzen2885 жыл бұрын
Hi Blackpenredpen, I have a question for you: When you write(for example) sin^-1(x), you mean 1/sin(x) or arc sin (x)?
@luqas80015 жыл бұрын
99% sure that its arcus. I struggle with the same problem everyday
@isaacaguilar56424 жыл бұрын
Typically arcsin(x) because we call the other one csc(x)
@DendrocnideMoroides5 жыл бұрын
When Dr.Peyam was parameterizing the line segment on the semi circle from (-R,R) he wrote that ( γ(t)=t) but what is the meaning of (γ(t)).
@MagicGonads4 жыл бұрын
(gamma(t)) is just enclosing it in brackets so it's easier to square without confusion gamma(t) is just some function of real t that outputs complex values it sorta represents how one might draw the curve in 2D using a pen and t is the time it takes to get to the point gamma(t) while drawing the curve (but the time can be any interval over the reals, it doesn't literally mean real world time since starting the curve, just an analogy) there might be some constraints like maybe it has to be continuous or not undifferentiable at measures greater than 0 or something like that but anyway since it's a real input function it can be differentiated using bounds of integration notation (if it is an integrable function) just like any real functions you would deal with in calculus or real analysis, just that the output space would may complex (in this case since gamma(t) = t which is always real)
@trafo222 Жыл бұрын
By the way I think you can do paramatrization this way too. Say z=x+i*y, from -R to R there is only real numbers so z=x if z=x then dz=dx. After that just put in place.
@deyomash3 жыл бұрын
I just always forgot why the semi circle is sufficient. Why not both poles have to be included. Because you can integrate using any curve? but you have to include at least 1 pole, clearly.. can't rememberrr
@elizabethmeghana96144 жыл бұрын
I really liked the host
@BrainsOverGains5 жыл бұрын
Did you make a mistake? The integral was 1/z^2 + 1 and you used the triangle inequality with 1/z^2-1?
@dank94275 жыл бұрын
1/abs(z^2+1)=1/abs(z^2-(-1)) We needed a subtraction here, and when we broke it up, abs(-1) just became 1
@bhaveshohal33904 жыл бұрын
Man... I love your smile 😍😅😛
@zacharyusher65775 жыл бұрын
"ok" - blackpenredpen 5/1/19
@blackpenredpen5 жыл бұрын
Zachary Usher ?
@Apollorion5 жыл бұрын
Can't this integral (i.e. from minus infinity to plus infinity of 1/(1+x^2) ) also be solved like this? 1: L=int(-inf,+inf, 1/(x^2+1) ) 1/(x^2+1) is even, so L can also be derived as 2 times the integral from 0 to infinity => 2: L=2*int(0,+inf, 1/(x^2+1) )=2*int(0,+inf, (1/(x+i))*(1/(x-i)) ) 3: f(x)=1/(x^2+1)=1/((x+i)*(x-i))=A/(x+i)+B/(x-i) => A=-B and -2Ai=1 => A=i/2=-B => 4: L=2*int(0,+inf, i/(2(x+i))-i/(2(x-i)) )=i*int(0,+inf, 1/(x+i)-1/(x-i) ) 5: F'(x)=2f(x)/i=1/(x+i)-1/(x-i) and so F(x)=ln|x+i|-ln|x-i|+C L=i*(F(+inf)-F(0) )=i*(lim( x->+inf, ln|(x+i)/(x-i)| ) - (ln(i)-ln(-i)) )=i*(0-i*pi/2-i*pi/2)=-i^2*pi=pi I wonder: how much am I doing (in)correct at step (4 to) 5 or maybe somewhere else?
@kevincardenas66294 жыл бұрын
Isn't it easier to use Cauchy's Integral Formula? with f(z)=(z+i)^-1 and w=i? you get the exact same result. Also this only works for R>1 right?
@GSHAPIROY5 жыл бұрын
Nice Big Classroom He Has There
@alexismandelias5 жыл бұрын
arctan(inf) - arctan (-inf) = π ?? I'd like an explanation please. You just glossed over that as if it's trivial
@blackpenredpen5 жыл бұрын
Alexis Mandelias arctan(inf) is pi/2 And arctan(-inf) is -pi/2
@alexismandelias5 жыл бұрын
@@blackpenredpen nvm I'm beyond stupid. I was thinking of a different function. Thanks for reply though
@RiteshKumar-sy9sp2 жыл бұрын
Can't we use Euler's form for z??..
@davidloomis66685 жыл бұрын
What course would you learn this in?
@joeaverage83295 жыл бұрын
Integration 101 Just Joking. You would learn this in Complex Analysis usually.
@hugoschmitter4765 жыл бұрын
Oke, it’s very interesting
@hamiltonianpathondodecahed52365 жыл бұрын
it flew , just over the cereberum
@yashovardhandubey52525 жыл бұрын
BPRP : "OK" Me : master saitama?
@francescocipriani88884 жыл бұрын
Are you also a doctor? , so do you have phd?
@غيثالأسعد-ي9ظ5 жыл бұрын
Wonderful 🌷
@gtmstev4 жыл бұрын
Why in that case the absolute value of z its iqual to R?
@jayapandey25415 жыл бұрын
I get it or should I say 2i get it.
@yoylecake3136 ай бұрын
why is it x in the title, not z?
@yoylecake3136 ай бұрын
oh, i commented before watching
@osamataha92525 жыл бұрын
please can help me to solve let a and b are matrices, if a*b=b*a prove that a*(b^-1)=(b^-1)*a
@bhuvird1785 жыл бұрын
Super u and Dr πr
@matefixfix13385 жыл бұрын
Okay
@brandonhh41115 жыл бұрын
🏳️🌈🏳️🌈🏳️🌈
@FaustoTube19724 жыл бұрын
I'm the like number 1000........yeeeeeeeeeeeeeeeeeeeeee ;-)
@dean109565 жыл бұрын
I umm... I have no clue what just happened.
@germangb87525 жыл бұрын
3:10 shouldn't it be absolute value abs(γ'(t)) in general?
@duckymomo79355 жыл бұрын
Yes He forgot it
@VibingMath5 жыл бұрын
Wow that starry night picture(wrong focus sorry)
@blackpenredpen5 жыл бұрын
Mak Vinci oh ok!! Hahaha
@VibingMath5 жыл бұрын
@@blackpenredpen Though that wont distract the great lesson by Dr. P 😁
@blackpenredpen5 жыл бұрын
Mak Vinci there’s another really cool picture, coming up soon
@p.singson39105 жыл бұрын
Talking about Starry Night, Please make a video chaos theory and turbulence.
@p.singson39105 жыл бұрын
Nice focus Mark, not a worthless one. There's a mathematical/physical backstory to it: accurate depiction of Turbulence.
@bouteilledargile5 жыл бұрын
i stan the pride flag in the background
@user-nb6zu3rk4f5 жыл бұрын
8:40
@rurafs79345 жыл бұрын
Wait wait... A rainbow flag 🤔🤔
@angelmendez-rivera3515 жыл бұрын
Rura FS Ye
@IanSwart5 жыл бұрын
Fags use it
@fuckyou16405 жыл бұрын
🌈 Your point is?
@ummwho82795 жыл бұрын
Well yeah, I mean I'm pretty sure Dr. Peyam is.... a wonderful human being and a gift from the heavens, duh. ;)
@hexeddecimals5 жыл бұрын
I got a little giddy when I saw that
@GUTY17295 жыл бұрын
Subtitules in spanish please!!!! Tranks.
@raincold54265 жыл бұрын
Oke
@JamesLaFleur5 жыл бұрын
Why is there this rainbow flag?
@fuckyou16405 жыл бұрын
Why not the rainbow flag? 🏳️🌈🏳️🌈🏳️🌈🏳️🌈
@sensei97675 жыл бұрын
June is pride month
@JamesLaFleur5 жыл бұрын
@@sensei9767 Thank you!
@JamesLaFleur5 жыл бұрын
@@fuckyou1640 Everyone should live how he wants to. But this is brainwashing. lbpost.com/wp-content/uploads/2017/10/DMN9oKgUIAAls6N.jpg
@sensei97675 жыл бұрын
@@JamesLaFleur 1. This doesn't have to do anything 2. How is education brainwashing? By that logic I could say that it's brainwashing if kids only lern about traditional families and relationships. 3. What's exactly your problem with that picture? You can't really see what those books are about, or is this about the outfit? If you want to have some sort of conversation you need to present your problem in some meaningfull way.
@anabang12515 жыл бұрын
In physics we learn this in 2nd semester lol.
@blackpenredpen5 жыл бұрын
Ana Bang 👍
@blackpenredpen5 жыл бұрын
We learn this in Peyam’s office.
@anabang12515 жыл бұрын
@@blackpenredpen Serious question: Did you really not know complex integration? You know so damn much about integration and maths in general, it's weird to see you struggle at sth. I can actually do^^
@blackpenredpen5 жыл бұрын
Ana Bang I kinda remember it but kinda don’t. I learned this like over 12 years ago and hadn’t touch it since then.
@sergioh55155 жыл бұрын
You learn complex integration in a physics class? 🤔
@ilouleoy75025 жыл бұрын
I get so lonely lonely lonely lonely lonely
@thephysicistcuber1755 жыл бұрын
Third
@GUTY17295 жыл бұрын
No entendí una pija pero vi todo el video 📹 por que se cagaban de risa 😂.
@oscartroncoso25855 жыл бұрын
First!
@DAOXINNo153 жыл бұрын
We stan with an LGBTQ+ math professors!
@High_Priest_Jonko5 жыл бұрын
Show the teacher some respect
@blackpenredpen5 жыл бұрын
Sydney Carton ?
@dharminderram52465 жыл бұрын
What?
@kaj6944 жыл бұрын
周知院学院 周知のじーじつ
@Abdalrhman_Kilesee Жыл бұрын
LGBTQ flag ? 😡
@Biggyweezer695 жыл бұрын
Anyone watch while playing minecraft?
@Biggyweezer695 жыл бұрын
@@mipmip4575 same trying to get into 2b2t rn
@DanielRamos-sl4kk5 жыл бұрын
Second
@sinpi63329 ай бұрын
disappointed
@backyard2825 жыл бұрын
I was just wondering... Is Dr Peyam gay?
@luisdaniel95425 жыл бұрын
I mean, the " 'i' don't like to be in the bottom" misunderstanding and the huge pride flag might mean something who knows