Laurent Series Explained | How to Determine Laurent Series | Complex Analysis #9

[@TheMathCoach]

Hello guys, did you know that I have the whole course covered (theorems + examples for all main concepts in short concised videos) in my complex analysis playlist on my channel, which I really hope can be useful to you guys learning the material: kzbin.info/aero/PLraTC6fSWOiptqOd_rMhFk6mZM30l7SqQ

[@Nightfold]

This video has everything you need to understand Laurent series and solve many problems. Perfect for when your teacher is completely useless

[@TheMathCoach]

Happy to help and glad that you found my content useful :)

[@uncommon2848]

@@TheMathCoach I

[@shivarammani6625]

Exactly... Same here.

[@xyz111xyz]

same, it is very sad that many universities dont really help students in learning...

[@aaronstone6183]

By far the best explanation of laurent series on you tube. thanks for help!

[@TheMathCoach]

Happy to help and thank you for your kind words, much appreciated!

[@georgeyu7987]

agree

[@igragarirg9728]

I have a Complex Analysis exam tomorrow and this video made me understand Laurent series better than any book/notes I've read. Than you!

[@TheMathCoach]

Happy to hear that! Best of luck with your exam tomorrow :)

[@TheMathCoach]

My first video ever to reach 100 000+ views, I'm really happy to be able to help so many people with mathematics!

[@thermrm]

you deserve the best!

[@ramonmerinorojas8535]

You can't imagine how much I love you rn, you saved my complex analysis course xd

[@TheMathCoach]

Happy to help!

[@shivarammani6625]

Amazing explanation. Came here completely confused - my prof didn't explain it at all - and am now as clear as I can be. Thanks!!

[@TheMathCoach]

Thanks! happy to hear that it worked out for you :)

[@thekingsoftube3087]

You are my savior, there’s no video/guide on the internet as precious as this video if you’re sarching for a clear and complete explanation of Laurent Series, thanks man!

[@TheMathCoach]

thank you my dear king, i really appreciate it!

[@pranavkrishnan2579]

This is a fantastic video and explanation. The pace (much faster than Khan Academy etc) actually helps, because it forces you to pay attention and helps you soak in the concepts and approaches better. Much thanks. Do keep making videos!

[@TheMathCoach]

I'm happy you liked it, thanks for the kind words :) I'm planning to one day continue!

[@alejandrosoto4930]

Finding these videos was like finding a treasure, thank you so much!!!!!

[@TheMathCoach]

I'm glad you liked it, enjoy!

[@alejandrosoto4930]

TheMathCoach Do you know where can I find information about multivalued functions? It gets difficult for me specially when i want to integrate them

[@TheMathCoach]

I have no video covering the subject at the moment. But I can recommend this video (kzbin.info/www/bejne/hnu0o4d5Zs-dm5I) by Barrus, I used to watch him when I took this course myself. If this still is not sufficient, then I recommend that you try to use this (math.stackexchange.com/questions/tagged/complex-analysis) math forum. It is really active, with a lot of helpful members and completely free of course. Hope this helps :)

[@isaackay5887]

Wow, what an excellent video!! There are some moving parts about Laurent Series I didn’t realize until just now*, but you've cleared up my frustrations. Thank you and well done!

[@TheMathCoach]

Happy that you found my content useful Isaac! and also glad that I could help out with all the small components that makes up laurent series :)

[@davidjohnson-my6sr]

Exam in 5 days, keen for this playlist!

[@TheMathCoach]

Good luck mate, I believe you can do it! Hope the playlist will be of use to you, just let me know if you got any questions about the topics I cover in the videos, I will be sure to answer frequently and to the best of my ability :)

[@briangallagher5698]

How'd the exam go?

[@TheJProducti0ns]

@@briangallagher5698 He switched majors and became a psych major lmfaoo (just teasing all psych majors out there)

[@hiveknight7416]

Clear and well explained, very beautiful handwriting too. Thanks for explaining what my prof cannot

[@TheMathCoach]

Happy to help! I'm proud of my handwriting :)

[@rodrigovelasquez8204]

i had no words to describe how much i have to thank you for videos! the beast explanation ever!!!!

[@TheMathCoach]

I think you did manage to express that pretty great with this message, thank you for the feedback :)

[@ranani20]

Dude that's the loveliest most Swedish accent if I ever have heard one! :D And Thanks for the vid, exam in two days, fingers crossed!

[@TheMathCoach]

Thank you and best of luck with your exam! :D

[@dhananjaymahajan3531]

loved it ! excellent and crispy explanation ...just to the point...keep going students like me needs teacher like you 📝🙌

[@TheMathCoach]

Ohh lovely! Happy to help and also glad that you found my format and content useful :D

[@jhumasarkar5203]

I understood one thing really well and that is Laurent series is hard as hell.

[@TheMathCoach]

Glad you took away something from the video :)

[@samuelmusyani7163]

Best elaboration of Laurent Series ever seen!

[@TheMathCoach]

Happy to be able to help!

[@elvis_mello]

That's a really good explanation! Concise listing of concepts and formulas, great use of colors to highlight important variables Thanks for spending so much time in this :)

[@TheMathCoach]

Thank you for the kind words :D Glad that my content is useful for you!

[@balazsvajda4278]

Thank you very much for this playlist! It helps so much! And it feels good to understand some things finally 🙏😄

[@TheMathCoach]

Happy to hear that and welcome to the channel, just let me know in the comments if you have any questions. I go through them all each sunday. All the main concepts are included in the playlist but I still have around 2-3 videos left to complete the course I think :)

[@SoumyadeepMisra7]

Best explanation of Laurent Series on youtube..

[@TheMathCoach]

Glad you think so! I'm happy to help out and bring more ways for people to understand the subject :)

[@ionutbum7799]

Ty, dude. My teacher couldn't implement this into my head like this video did. Helpful!

[@TheMathCoach]

I don't blame him, Laurent Series is a tricky concept ^^

[@raintrain9921]

I really hope you start making videos again, I would love to see your explanations of different topics in higher level math.

[@TheMathCoach]

Happy you like my teaching methods and I would also like to get the motivation and time to create videos again. I might come back in the future, I at least have to finish the video I started making about 1-1.5 years ago.

[@Trombi01]

You save lives with videos like these

[@TheMathCoach]

Happy to be saving lifes from my computer :)

[@dannyson9602]

This is absolutely amazing. Thank you so much!

[@TheMathCoach]

I'm glad you liked it! :)

[@溜溜梅-l4z]

THANKS!! Now I really understand why geometric series is so important!

[@TheMathCoach]

Its is the real deal :)

[@georgepefanis9278]

You helped me understand laurent series. This video had everything I needed. Thank you

[@TheMathCoach]

I'm just happy to help and I'm glad you liked it :)

[@batres8573]

you should have a million followers o more, this was a really good explanation , you rock!!!!

[@TheMathCoach]

thank you for the kind words, it warms me up! :)

[@ALBAGetos]

Man thank you, Laurent series were giving me a serious headache but it's wayyyy clearer now. Also wanted to say the quality of this vid is insanely good, like props to you.

[@TheMathCoach]

Happy to hear that you found my content helpful! thank you, I'm quite proud of my handwriting and storytelling here :)

[@Saqlain01]

Thankyou so much sir, I searched alot , this is the only video available for this concept.

[@TheMathCoach]

Happy to help out, I also like my video about Laurent Series, one of my favorites!

[@guest9580]

What takes lecturers 3 hours to teach, you teach in 13 minutes. Good job sir

[@TheMathCoach]

I'm glad to hear that, good sir!

[@aneeshaavasthi554]

Your presentation is EXTREMELY good and the concepts are also taught VERY well. I have a friendly tip though. If you could add some voice modulations or perhaps simply pause before you bring up an important or note-worthy point, it would help break the monotony. This would keep the viewers engaged. Anyway, I am grateful for finding your video. Thank you.

[@TheMathCoach]

Thank you so much for the kind words and for the tip, I will see if I can implement it in future videos :)

[@danielzhicool8048]

Thanks for this great video! Helped me a lot in preparing for the exam.

[@TheMathCoach]

Hope it went well and you keep on learning!

[@PunmasterSTP]

Another phenomenal video! I have to go to sleep now (I've already stayed up a bit too late to watch these), but I will be back tomorrow for sure!

[@TheMathCoach]

Good night!

[@reubenwilliammpembe667]

4 days to go for my final exam in engineering mathematics 2 and special thanks goes to you Sir. You are the best keep up the good work!! #RespectFromSouthAfrica

[@TheMathCoach]

Happy to hear that you find my content useful and *best of luck* to you with your exam!

[@anushkachaturvedy3624]

Thank you for this. I've been looking for these type of questions, and I found it here. Great explanation, easy breezy.

[@TheMathCoach]

I'm happy that to help!

[@shayanhooshmand506]

your videos are best ones for learning among all youtube videos. keep your good work.

[@TheMathCoach]

Thanks a ton! There are a lot of great content creators on this platform :)

[@rickpala_]

this video saved my grade in complex analysis

[@TheMathCoach]

I'm glad I could help you with your grade :)

[@zhikunli475]

The CA course in my university provides no explanation and expects us to figure out how to determine the Laurent series on our own😅 This KZbin video is literally twice as good as what I get in Uni which my parents payed tens of thousands of pounds for, Bravo to the education system 👍

[@isabellacastellanosazuero9404]

Thank you so much for the help! It is by far the best video on this topic

[@NicolasSchmidMusic]

You and faculty of khan are just the best in this topic. And your videos look pretty similar :)

[@TheMathCoach]

He makes a lot of informative videos, you have a great taste my dear sir. I think we both were inspired by Khan Acadamy's style.

[@mrpabloskyoskosky]

Thank you for saving my life!

[@TheMathCoach]

I should reconsider going into the life saving bussiness!

[@alcatraz5161]

Beautifully explained Helped me out in the last throes of my complex analysis mandatory assignment : D Godspeed to you

[@TheMathCoach]

Wonderful! Happy to help :)

[@redgremlin2162]

Extremely helpful man! Thanks!

[@TheMathCoach]

My pleasure :D

[@haneenmohamed5938]

Thank you so much الله يجزيك خير ويهديك للحق، فهمتني الموضوع الصعب دا🤍🤍

[@jonaargueta771]

This video is exactly what we wanted

[@TheMathCoach]

That is great to hear, happy to help!

[@SubrataGhanty]

Amazing explanation... Love from 🇮🇳

[@TheMathCoach]

Glad to hear that you liked it! Love from swe

[@physicsdepartmentuniversit8770]

your writing style is awesome

[@TheMathCoach]

Thank you so much 😀 I have practiced it for a long long long time :D

[@willovecali_0208]

You save my exam tomorrow, THX

[@TheMathCoach]

Hope your exam went well will :)

[@Paul-jq1wo]

After a lot of desperation you helped me so much, thanks!

[@TheMathCoach]

Glad you could leave the desparation behind you!

[@nazaninghelichi5240]

Life saving video! Amazing explanation and everything. Thanks man

[@TheMathCoach]

Happy to save lifes! Have a great day and best of luck with your studies :)

[@brandonk2465]

I love your video but I have a question. 7:06, in the first problem you did b = 2 , but I thought the condition or rule that is necessary is that the absolute value of W ( which is 2 ) has to be greater than b and not equal. Since the absolute value of b is equal 2 doesn't that obstruct the rule that absolute value of b has to be less than absolute value of W?

[@TheMathCoach]

Happy you find my content useful and thanks for the question, let me try to clear this up for you. You are completely right about that W must be greater than the absolute value of b (which is 2 in this case as you stated) if we want to use the formula. In this case, W is our argument for the complex function (you can think about W as Z if that makes it easier) and this argument can *not* be equal to 2 since we said at the beginning of the problem that we only are looking at the domain *IzI > 2*. Hope this clarifies it!

[@bekiryufka]

just before exam! Thx a lot.

[@TheMathCoach]

I hope you did well on the exam!

[@ericelms7038]

Thank you for the great explanation! One thing I'm curious about is why we did the expansions around 0 and 1; since there is a singularity at 2, wouldn't we want to do the expansion around that point?

[@teriyaki8643]

You are reading z_0 as z_NUT 😂 I'm sorry, it just made my day. Thank you for the very helpful explanation of the topic.

[@TheMathCoach]

Happy I could make your day better, and I hope you are having a great day today too, and othervise you could also come back here for a quick laugh :)

[@hamsalak9779]

holy mate that was some clean explanation. Tnx

[@jeonghyeokim1017]

This is so well done man im crying rn

[@TheMathCoach]

tears of joy I hope :)

[@tubagusdaffaxi1216]

Thank you very much. You are the best

[@TheMathCoach]

you are the best for wanting to learn!

[@haaniaaamir8297]

Such an easy to follow and clear explanation!!

[@TheMathCoach]

I'm happy to help, glad you liked it :)

[@praptikumarvishwakarmavvuc4608]

NIce Explanation. Thank You

[@TheMathCoach]

Glad it was helpful!

[@jokingseverus3221]

Another awesome and helpful video to learn with a compact as well as attractive way of learning... thank you sir...

[@TheMathCoach]

Ohh I'm happy that you are sticking around here and that I was able to help you out two times in one day! Thank you for your kind words :)

[@jokingseverus3221]

TheMathCoach thank you sir... actually I am lucky that I find all that I need... next target is contour integration...😊

[@TheMathCoach]

Ops, forgot to reply here! Hope your contour integration reviewing went well :)

[@tarumpalo]

Thank you. This helped me a lot and you are really great at explaining.

[@TheMathCoach]

I'm happy that you found it useful :)

[@IT--rz3br]

very good video. Thank you so much . it really helped me to gain more profound knowledge about laurent series

[@TheMathCoach]

I'm happy to help!

[@saradagunasekara2638]

Thank you very much for the clear explanation... very much helpful

[@TheMathCoach]

I'm happy to help :)

[@xyz111xyz]

thank you very much, finally know what's going on with R,r :D

[@TheMathCoach]

Happy to help out! Sometimes an image is all one needs ^^

[@Higgsinophysics]

Cyrstal clear. Thank you for sharing

[@TheMathCoach]

My pleasure!

[@creweune7059]

Thanks for the video, it is really helpful for this topic.

[@TheMathCoach]

Happy to help Crew! :)

[@arnaudleclef2021]

Thank you for this video, it helped me a lot! :-)

[@TheMathCoach]

I'm happy to help!

[@lmatton1]

Excellent explanation- thank you!!

[@TheMathCoach]

I'm glad that you found it useful :)

[@pranitashinde9228]

Thank you sir for such an amazing lecture.

[@TheMathCoach]

Happy you liked it!

[@MrKampfwurst]

Great Explanation! Helped me a ton!

[@TheMathCoach]

I'm happy to hear that!

[@chesterfielded]

Excellent video - helpful effects, clear handwriting and speech, having the formulae in the corner is very helpful. You could be a little more clear on the fact that some of the series being derived for certain domains are turning out to be only the analytic/principal parts for examples 1) and 2), but small detail. Thank you for posting.

[@TheMathCoach]

I'm happy to help and also thank you for the superb feedback. This is exactly the kind of information I need to improve my content, since this helps me understand what works and what doesn't. Thanks for leaving an comment :)

[@ahmadjafararifi5575]

it's a clear explanation, very helpful.

[@TheMathCoach]

Happy you liked it.

[@ranadipsaha3130]

Thank you so much for helping out

[@TheMathCoach]

Happy to help!

[@shaun4.]

Great lesson!

[@TheMathCoach]

Glad you liked it!

[@dicksonkibe9894]

best explanation of laurent sweries of expansion.cudoz

[@TheMathCoach]

Happy to help. Thanks for the kind words :)

[@euler0148]

continue! you are a legend

[@TheMathCoach]

Happy to help! Next video coming out this Sunday :)

[@euler0148]

@@TheMathCoach thank you for that. happy new year

[@TheMathCoach]

@@euler0148 My pleasure, happy new year

[@daniloup8139]

Thank you very much, very helpful information 👍

[@TheMathCoach]

I'm just happy to help!

[@shingen911]

Good timing! My exam is in two days :)

[@TheMathCoach]

I got you covered mate! Best of luck to you with your exam and I hope this video playlist can be useful to you :) Also feel free to let me know if you have any questions regarding complex analysis in general, I will be sure to help you the best I can!

[@topzio5265]

it's is help full video thanks a lot!

[@TheMathCoach]

Glad it helped!

[@AraDeanMaffy]

Excellent, well done episode! ... congratulations again ;)

[@TheMathCoach]

Thanks, I'm so glad to see that you are coming back to keep watching my videos and I also thought this episode was rather good, so I'm glad someone else agreed with me there aswell :)

[@armchair8258]

You explain so well, thanks!!

[@TheMathCoach]

No problem, I'm glad you liked it :)

[@frechernono6401]

Really well expleained! Thank you

[@TheMathCoach]

Happy to help!

[@alexx1642]

Thank you! It was the point I didn't get in complex analysis, you literally saved my life! (Well, rather my exam than my life, but it's still a lot)

[@TheMathCoach]

That is kind of the same thing for a uni-student so I completely understand you, I'm glad I could help and good luck with your exam!

[@Vanilla2903]

Watching this one hour before my exam

[@TheMathCoach]

Hello mate, how did it go? I Guess you nailed the Laurent Series questions on your exam. Happy Holidays!

[@fabriziavigna8614]

great video , very clear

[@TheMathCoach]

Glad it was helpful!

[@tuongdihoc]

Thank you again!

[@TheMathCoach]

Any time!

[@williamronayne6462]

This has saved me. My thanks.

[@TheMathCoach]

I'm happy to help :)

[@irfanjames6551]

Thanks You're Amazing

[@TheMathCoach]

Happy to be able to help out!

[@3r3bu5x9]

wow...found just what i needed

[@TheMathCoach]

sometime you got to be lucky :D

[@tombushell6581]

Great video! Though I am still confused as to how the Laurent series actually differs from using a taylor series thou - you just seem to be using the standard power series to do your expansions (in my eyes at least lol) :/ All of your examples have the singularity on the contour of the domain? Isnt the Laurent series used for when you are finding a series about z0 which is the singularity itself (inside the domain)?

[@TheMathCoach]

Happy to help out Tom and great question! The main difference between Laurent Series and Taylor Series is that Laurent Series are able to "capture" (another way to see about it is that it avoids) isolated singularities by the help of the "annulus" domain. In all the examples we used in the video we defined the regions such that the isolated singularities were just outside of these regions, for example in the first example we used that we took all z values with an length bigger or smaller then 2 but not exactly 2 since that would means that the singularity was included in the region. We could have had a singularity at the point that was the center for the expansion and it would make no difference, the main point is that Laurent Series gives us the freedom to "capture" the isolated singularites and therefore exclude these points from the series itself. I hope it helps clarify!

[@cdirfe947]

Your handwriting is so beautiful.

[@TheMathCoach]

I uploaded my IRL handwritting to the community tab on my channel if you want to see if it matches, I'm proud of my handwritting :)

[@omaraburashed6824]

great video.. thanks a lot

[@TheMathCoach]

Glad you liked it!

[@yusufkanat3260]

Thank you so much my friend👍👍👍

[@TheMathCoach]

I'm just happy to help!

[@ethiopiansickness]

Great explanation, but I have a question. At 6:05 you factored out a negative 1/2 but at 6:56 you factored at a 1/z. I'm confused as to why you use different factors. Thank you

[@TheMathCoach]

Hi, happy you liked the explanation and that you voiced your question. The different kind of factors comes from the fact that we have two different kinds of denominators (2-z versus z-2) in the two problems. To be able to use the geometric series we have to rewrite the problems on the same for as the formulas and that is why we factor out in the first place, we are therefore trying to create a denominator that looks like (*1* - X) where X changes depending if we wanna use formula (1*) or (2*). With this in mind, we can see that we factored out (-1/2) in the first problem because we wanted to create the number *1* in the denominator but we would not be able to use the same factor for the second problem since the numbers in the denominator is switched around in that problem (z-2 instead of 2-z) and therefore we have to factor out 1/z to create the number *1*. All of this is however done to rewrite the problems so that they match the expression used in the formula so that we can use them. Hope it helps!

[@ethiopiansickness]

TheMathCoach Thank you so much for your thorough response it is greatly appreciated. I understand it now very clearly. I want to pursue particle physics, so I’m taking a summer course in complex analysis. It has great applications in physics. Thank you again !

[@TheMathCoach]

Happy to help and good luck with your summer course, it sounds like a great decision to take early on :)

[@ethiopiansickness]

Hello Math Coach, thank you for a great video. I just have a question about 7:21. I don't understand when and why you should change the limits of the summation. I've seen this phenomenon occur for other solved problems that I've seen. When should we change the limits of the summation? You changed the lower limit from n = 0 to n = 1. thank you. Also at 5:08 in the top right corner ( small box with formulas) what do the (1^x) and the (2^x) represent ?

[@TheMathCoach]

Hello, happy you liked it. I only changed it here since the *principal part* (which is the part we are working with here in this example) is defined to start from n=1 but our summation started at n=0, therefore we needed to change it otherwise it would the summation could not be the principal part of the Laurent Series since it was not written in the correct form. The symbols (1*) and (2*) is the notation/names I gave the formulas (1* = the first formula, etc.) so it would be more clear in the video which one I'm referring to when doing the examples. Hope it clarified it!

[@laupii1]

Awesome explanation, thanks.

[@TheMathCoach]

No problem, I got you covered. Glad to see you browsing through some videos, welcome to my channel mate. I have always found it kind of weird why most of the videos online never really explains why we use these geometric series and how to apply them to a specific problem. That is why I thought it would be kind of nice to cover these two parts in depth and I'm glad that this explanation was useful to you!

[@MesbahSalekeen]

thanks man......

[@TheMathCoach]

No problem mate.....

[@VNFilmography]

Thank you sir...

[@TheMathCoach]

Happy to help out and I hope you are having a great day :)

[@ttinytinaaaa6089]

thanks for making this vdo!

[@TheMathCoach]

Happy to help!