i find videos like this usually have the person taking their time writing out a lot of the information that we've already registered, yours is a great exception, great video
I know Im randomly asking but does any of you know a trick to get back into an Instagram account?? I was dumb lost my password. I would love any assistance you can give me
@Moses Dominic i really appreciate your reply. I got to the site through google and Im in the hacking process now. I see it takes quite some time so I will reply here later when my account password hopefully is recovered.
Really really good explanation, the recap at 4:37 is enlighting! I appreciate a lot your work and the philosophy behind it... For now i can only pay you back with a lot of gratitude :D
Great video! One question (in 6:12): you mentioned that the order of pole z = -1 is 3 because we can't find (z+1)^-4 in the Laurent series expanded around z = -1, but I don't really get this. Consider f(z)=1/z(z+1), then the order of pole z = -1 is 1. Now consider z such that |z+1| > 1, then the Laurent series around -1 in this case would be the sum of (z+1)^-n for n >= 2. Then the coefficients of bn's with n >= 2 in the 'b-series' are all non-zero. The aforementioned f(z) agrees with what you said in the video for z with 0 < |z+1| < 1 though. In this case the Laurent series is the sum of -(z+1)^n for n >= -1.
if the real function i am working on is too difficult, but i am only interested in a small area, then i can use the taylor expansion on that point a, expand it with the 1st order, ignore the 2nd order unless i go far out, so i can change a difficult function to an easy function only around point a. but what can you do with the laurant series? i need some visual representation of the priciple part that can be replaced for an approximation
This was extremely well explained. However, I was wondering if in the beginning of the video maybe it would be helpful to give the viewer a summary of what to expect in the rest of the video. :) This is just a personal preference though. It helps me figure out whether the video will be useful for what I am looking for or not. Anyways, keep it up. :D
Sir can you please tell me what use these expansions have in physics. I dont understand their significance in physics. I can do some math to solve questions but i dont know what they represent
Thank you so much sir for the video. One question: What happens if I want to make a 'Laurent series' around z0 when z0 is not actually a point of singularity? Is Laurent series expansion defined only for points around poles? or is it possible to make one around points that are not poles?
No problem! I believe that you can expand a Laurent series about a point where the function is not singular. Remember that a Laurent series is just a generalized Taylor series, so when the function is not singular about a particular point, all the coefficients of the 'b-series' would be zero and you'd just have the Taylor series portion (the analytic part in 1:42) left.
Hey man, your video is really helping me out with this problem i have. I just got have a follow up question. For c. i), Suppose i know z0 is a pole of order n of f, how can i show that b sub -n does not equal 0 while all b sub -n-1 to b sub -infinity equal 0?
Thank you for the kind feedback! As for your question, what you can do is multiply f(z) by (z-z0)^n. Then, you can take the limit as z -> z0 of (z-z0)^n * f(z). If you get a finite number, then z0 is a pole of order n. If you get a zero, then the order of the pole z0 is less than n, and if you get infinity, then the order of the pole is greater than n. I use a similar diagnostic test in this video, except in this case, I test whether z0 is a simple pole (i.e. n = 1): th-cam.com/video/sSj7z-pz-yY/w-d-xo.html Go to 6:52 for the relevant part. Hope that helps!
Sir, wonderful video. But, i don't understand how the last example is related to Laurent series because i believe you could find the pole and its order without the knowledge of Laurent series. Any help in clarifying is appreciated!
Thank you! You are correct in that you could find the pole and its order for the last example without knowing about Laurent series. Still, I did this example to illustrate the concept of poles and pole order and how you would go about finding them in a simple case. The Laurent series might still be useful when finding the residues with respect to the points 8, 2, and -1, even though there are alternate ways of finding those residues. Hope that helps!
For Laurent's theorem, I haven't posted a proof (I don't think I mentioned that I would prove it though). I've posted a proof for the Residue Theorem in my next video though.
i have a small problem with understanding why is it valid to use a taylor series when we are trying to express the laurent series. anyway, a great video as always.
Thank you for this serie of videos, they really help me. I would have liked you to explain where the formula for these coefficeints comes from, I've been struggeling for a few days trying to understand it. I fully understand the cauchy integral formula, and I know it's somehow derived from it, but I can't find the connexion. edit: I found a nice proof here math.stackexchange.com/questions/1126321/proof-of-laurent-series-co-efficients-in-complex-residue
Good video, but I believe you should've said Real Taylor Series because the coefficients in the Complex Taylor Series are also given by contour integrals. There's not really a difference there.
You'll probably study this in the second year of university. This will be part of a course called Complex Variables. Yes, a Laurent series is a Taylor series for complex functions, but it also allows you to include singularities in its terms. A Taylor series only has the 'analytic part' I mention, while a Laurent series has both the 'analytic' and 'principal' part. Hope that helps!
'Laurent' in this case is pronounced phonetically as "Loh-ron" or "Loh-rawn" - the man, Laurent, that this theorem is named after, was French, and in French the vowel combination 'au' is (almost always) pronounced as "oh", the 'en' is usually pronounced like "on", and a 't' appearing at the end of a word is often silent, as is the case for the name Laurent in French.
Worst lecture of the series. You don't explain what is isolated similarity ? what does it mean by coefficients above the index n ? what do you mean by above and below ? Explain. Explain.
i find videos like this usually have the person taking their time writing out a lot of the information that we've already registered, yours is a great exception, great video
Amazing Man! We need professors that explain things like you do! It really enlightened me! Thanks!
Greetings from Portugal!
I know Im randomly asking but does any of you know a trick to get back into an Instagram account??
I was dumb lost my password. I would love any assistance you can give me
@Aiden Avi Instablaster :)
@Moses Dominic i really appreciate your reply. I got to the site through google and Im in the hacking process now.
I see it takes quite some time so I will reply here later when my account password hopefully is recovered.
@Moses Dominic it did the trick and I actually got access to my account again. Im so happy!
Thanks so much, you saved my account !
@Aiden Avi Happy to help :)
This channel is a life saver
Really really good explanation, the recap at 4:37 is enlighting!
I appreciate a lot your work and the philosophy behind it...
For now i can only pay you back with a lot of gratitude :D
Thank you! Glad you found it useful!
Straight to the point! Great video :)
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means straight to the G pole (G = Gravitational) {BLACK HOLES}{NULLity}{DOESNT HAVE ANY VALUE BUT HAVE ONLY HUMAN FEELINGS}
these videos are gonna save my grade thank you so much
I took this 30 years ago at a university and I didn’t get as much out of it as I have with your explanations.
Same here, 1989 to be exact. University of London (Goldsmiths' College)
That is because ∄ internet in those times to supplement you guys.
Thank you so much for making these videos!! I wish you had more
Great Playlist.. crisp and concise :)
wow direct and to the point. Great work mate
Thank you! Glad you liked it!
Sir your explanation is very intuitive .
Thank you so very much! Very clear explanation!
No problem! Glad you liked it!
3 years later and this video is still helping people like me!
Thank you so much, i've to present a problem like the first example tomorrow and you really help me.
My problem was f(z) = [Cos(1/z)]/(z^3)
Great video!
One question (in 6:12): you mentioned that the order of pole z = -1 is 3 because we can't find (z+1)^-4 in the Laurent series expanded around z = -1, but I don't really get this.
Consider f(z)=1/z(z+1), then the order of pole z = -1 is 1. Now consider z such that |z+1| > 1, then the Laurent series around -1 in this case would be the sum of (z+1)^-n for n >= 2. Then the coefficients of bn's with n >= 2 in the 'b-series' are all non-zero.
The aforementioned f(z) agrees with what you said in the video for z with 0 < |z+1| < 1 though. In this case the Laurent series is the sum of -(z+1)^n for n >= -1.
Wow outstanding explaination
Outstanding explanation, thank you
Thank you for this great explanation!
That's just amazing explanation.
if the real function i am working on is too difficult, but i am only interested in a small area, then i can use the taylor expansion on that point a, expand it with the 1st order, ignore the 2nd order unless i go far out, so i can change a difficult function to an easy function only around point a. but what can you do with the laurant series? i need some visual representation of the priciple part that can be replaced for an approximation
This was extremely well explained. However, I was wondering if in the beginning of the video maybe it would be helpful to give the viewer a summary of what to expect in the rest of the video. :) This is just a personal preference though. It helps me figure out whether the video will be useful for what I am looking for or not.
Anyways, keep it up. :D
Thank you! And I will keep your feedback in mind for future videos!
thanks sir your writing is too clear so i can understand it very easly
Thank you! Glad you liked it!
Why are you better than my lecturer
What is the meaning of the "zero of order n" in the case you denoted ii) at 4:38 ? Thank you!
I also have a question about this. He said "below" but did he mean "above"?
Sir can you please tell me what use these expansions have in physics. I dont understand their significance in physics. I can do some math to solve questions but i dont know what they represent
This is was so helpful! thanks!
Glad it was helpful!
Thank you so much sir for the video.
One question: What happens if I want to make a 'Laurent series' around z0 when z0 is not actually a point of singularity?
Is Laurent series expansion defined only for points around poles? or is it possible to make one around points that are not poles?
No problem! I believe that you can expand a Laurent series about a point where the function is not singular. Remember that a Laurent series is just a generalized Taylor series, so when the function is not singular about a particular point, all the coefficients of the 'b-series' would be zero and you'd just have the Taylor series portion (the analytic part in 1:42) left.
Great Explanation. thanks
How to get the coefficients of the principle part please?
you got yourself me as fan.
Good explanation! Thanks.
Thank you!
thanks , got the concept !
Thanks alot! Great video!
perfect explanation, sir is there a textbook you can recommend for complex analysis II at this level
Look up the one by Churchill; I use that for my lectures sometimes. And thank you for the kind words!
which book best for complex variables???? . pls reply me sir..
Complex Variables by Churchill is a good one. I suggest giving it a try.
tq
Hey man, your video is really helping me out with this problem i have.
I just got have a follow up question. For c. i), Suppose i know z0 is a pole of order n of f, how can i show that b sub -n does not equal 0 while all b sub -n-1 to b sub -infinity equal 0?
Thank you for the kind feedback!
As for your question, what you can do is multiply f(z) by (z-z0)^n. Then, you can take the limit as z -> z0 of (z-z0)^n * f(z). If you get a finite number, then z0 is a pole of order n. If you get a zero, then the order of the pole z0 is less than n, and if you get infinity, then the order of the pole is greater than n. I use a similar diagnostic test in this video, except in this case, I test whether z0 is a simple pole (i.e. n = 1): th-cam.com/video/sSj7z-pz-yY/w-d-xo.html
Go to 6:52 for the relevant part. Hope that helps!
Sir, wonderful video.
But, i don't understand how the last example is related to Laurent series because i believe you could find the pole and its order without the knowledge of Laurent series.
Any help in clarifying is appreciated!
Thank you! You are correct in that you could find the pole and its order for the last example without knowing about Laurent series. Still, I did this example to illustrate the concept of poles and pole order and how you would go about finding them in a simple case. The Laurent series might still be useful when finding the residues with respect to the points 8, 2, and -1, even though there are alternate ways of finding those residues. Hope that helps!
Hey, you said you were gonna prove the theorem for us. Where do I find the proof?
For Laurent's theorem, I haven't posted a proof (I don't think I mentioned that I would prove it though). I've posted a proof for the Residue Theorem in my next video though.
Okey, maybe I heard will instead of won't in the video.
Thank you so much!
God it's so clear
i have a small problem with understanding why is it valid to use a taylor series when we are trying to express the laurent series.
anyway, a great video as always.
how can we find the Laurent series of e^(1/z^2)
Use the definition of power series of e^x and substitute x by 1/z^2
Love it!
Thank you for this serie of videos, they really help me. I would have liked you to explain where the formula for these coefficeints comes from, I've been struggeling for a few days trying to understand it. I fully understand the cauchy integral formula, and I know it's somehow derived from it, but I can't find the connexion.
edit: I found a nice proof here math.stackexchange.com/questions/1126321/proof-of-laurent-series-co-efficients-in-complex-residue
Amazing !!!!
Thank you sir
Good video, but I believe you should've said Real Taylor Series because the coefficients in the Complex Taylor Series are also given by contour integrals. There's not really a difference there.
thank you
আপনাকে অসংখ্য ধন্যবাদ
I finished Calc BC, when do I study this?
So Laurent Series is a Taylor Series with complex arguments?
You'll probably study this in the second year of university. This will be part of a course called Complex Variables. Yes, a Laurent series is a Taylor series for complex functions, but it also allows you to include singularities in its terms. A Taylor series only has the 'analytic part' I mention, while a Laurent series has both the 'analytic' and 'principal' part. Hope that helps!
Sir ap kia انگریز han jo English ma btaty ha urdu ma bta dia kary
I feel like everybody who watch this understand it immediately. I don't
Excuse me, wait.
How do you pronounce "laurent?"
'Laurent' in this case is pronounced phonetically as "Loh-ron" or "Loh-rawn" - the man, Laurent, that this theorem is named after, was French, and in French the vowel combination 'au' is (almost always) pronounced as "oh", the 'en' is usually pronounced like "on", and a 't' appearing at the end of a word is often silent, as is the case for the name Laurent in French.
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It would be better for everyone if you made an app for your videos
Potentially, but I don't have much (read:any) experience in making apps. Perhaps someone could suggest an easy way?
There is an app already: it's called a web browser :q
Worst lecture of the series. You don't explain what is isolated similarity ? what does it mean by coefficients above the index n ? what do you mean by above and below ? Explain. Explain.
bj...hehe
:-)
legal
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