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: kzitem.info/door/PLraTC6fSWOiptqOd_rMhFk6mZM30l7SqQ
@Nightfold
5 жыл бұрын
This video has everything you need to understand Laurent series and solve many problems. Perfect for when your teacher is completely useless
@TheMathCoach
5 жыл бұрын
Happy to help and glad that you found my content useful :)
@uncommon2848
5 жыл бұрын
@@TheMathCoach I
@shivarammani6625
4 жыл бұрын
Exactly... Same here.
@xyz111xyz
Жыл бұрын
same, it is very sad that many universities dont really help students in learning...
@aaronstone6183
6 жыл бұрын
By far the best explanation of laurent series on you tube. thanks for help!
@TheMathCoach
6 жыл бұрын
Happy to help and thank you for your kind words, much appreciated!
@georgeyu7987
4 жыл бұрын
agree
@igragarirg9728
4 жыл бұрын
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
4 жыл бұрын
Happy to hear that! Best of luck with your exam tomorrow :)
@TheMathCoach
3 жыл бұрын
My first video ever to reach 100 000+ views, I'm really happy to be able to help so many people with mathematics!
@thermrm
2 жыл бұрын
you deserve the best!
@ramonmerinorojas8535
4 жыл бұрын
You can't imagine how much I love you rn, you saved my complex analysis course xd
@TheMathCoach
4 жыл бұрын
Happy to help!
@shivarammani6625
4 жыл бұрын
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
4 жыл бұрын
Thanks! happy to hear that it worked out for you :)
@pranavkrishnan2579
6 жыл бұрын
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
6 жыл бұрын
I'm happy you liked it, thanks for the kind words :) I'm planning to one day continue!
@thekingsoftube3087
3 жыл бұрын
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
3 жыл бұрын
thank you my dear king, i really appreciate it!
@davidjohnson-my6sr
7 жыл бұрын
Exam in 5 days, keen for this playlist!
@TheMathCoach
7 жыл бұрын
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
4 жыл бұрын
How'd the exam go?
@TheJProducti0ns
3 жыл бұрын
@@briangallagher5698 He switched majors and became a psych major lmfaoo (just teasing all psych majors out there)
@alejandrosoto4930
6 жыл бұрын
Finding these videos was like finding a treasure, thank you so much!!!!!
@TheMathCoach
6 жыл бұрын
I'm glad you liked it, enjoy!
@alejandrosoto4930
6 жыл бұрын
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
6 жыл бұрын
I have no video covering the subject at the moment. But I can recommend this video (kzitem.info/news/bejne/sYCH2Ih5apybmGU) 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 :)
@dhananjaymahajan3531
6 жыл бұрын
loved it ! excellent and crispy explanation ...just to the point...keep going students like me needs teacher like you 📝🙌
@TheMathCoach
6 жыл бұрын
Ohh lovely! Happy to help and also glad that you found my format and content useful :D
@elvis_mello
5 жыл бұрын
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
5 жыл бұрын
Thank you for the kind words :D Glad that my content is useful for you!
@isaackay5887
2 жыл бұрын
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
2 жыл бұрын
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 :)
@hiveknight7416
2 жыл бұрын
Clear and well explained, very beautiful handwriting too. Thanks for explaining what my prof cannot
@TheMathCoach
2 жыл бұрын
Happy to help! I'm proud of my handwriting :)
@raintrain9921
5 жыл бұрын
I really hope you start making videos again, I would love to see your explanations of different topics in higher level math.
@TheMathCoach
5 жыл бұрын
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.
@rodrigovelasquez8204
5 жыл бұрын
i had no words to describe how much i have to thank you for videos! the beast explanation ever!!!!
@TheMathCoach
5 жыл бұрын
I think you did manage to express that pretty great with this message, thank you for the feedback :)
@ranani20
3 жыл бұрын
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
3 жыл бұрын
Thank you and best of luck with your exam! :D
@balazsvajda4278
3 жыл бұрын
Thank you very much for this playlist! It helps so much! And it feels good to understand some things finally 🙏😄
@TheMathCoach
3 жыл бұрын
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 :)
@dannyson9602
6 жыл бұрын
This is absolutely amazing. Thank you so much!
@TheMathCoach
6 жыл бұрын
I'm glad you liked it! :)
@ALBAGetos
3 жыл бұрын
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
2 жыл бұрын
Happy to hear that you found my content helpful! thank you, I'm quite proud of my handwriting and storytelling here :)
@aneeshaavasthi554
4 жыл бұрын
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
4 жыл бұрын
Thank you so much for the kind words and for the tip, I will see if I can implement it in future videos :)
@georgepefanis9278
5 жыл бұрын
You helped me understand laurent series. This video had everything I needed. Thank you
@TheMathCoach
5 жыл бұрын
I'm just happy to help and I'm glad you liked it :)
@Saqlain01
Жыл бұрын
Thankyou so much sir, I searched alot , this is the only video available for this concept.
@TheMathCoach
7 ай бұрын
Happy to help out, I also like my video about Laurent Series, one of my favorites!
@samuelmusyani7163
8 ай бұрын
Best elaboration of Laurent Series ever seen!
@TheMathCoach
7 ай бұрын
Happy to be able to help!
@Trombi01
5 ай бұрын
You save lives with videos like these
@TheMathCoach
3 ай бұрын
Happy to be saving lifes from my computer :)
@jhumasarkar5203
3 жыл бұрын
I understood one thing really well and that is Laurent series is hard as hell.
@TheMathCoach
3 жыл бұрын
Glad you took away something from the video :)
@batres8573
Жыл бұрын
you should have a million followers o more, this was a really good explanation , you rock!!!!
@TheMathCoach
Жыл бұрын
thank you for the kind words, it warms me up! :)
@ericelms7038
2 жыл бұрын
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?
@SoumyadeepMisra7
Жыл бұрын
Best explanation of Laurent Series on youtube..
@TheMathCoach
Жыл бұрын
Glad you think so! I'm happy to help out and bring more ways for people to understand the subject :)
@PunmasterSTP
3 жыл бұрын
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
3 жыл бұрын
Good night!
@guest9580
4 жыл бұрын
What takes lecturers 3 hours to teach, you teach in 13 minutes. Good job sir
@TheMathCoach
4 жыл бұрын
I'm glad to hear that, good sir!
@shayanhooshmand506
3 жыл бұрын
your videos are best ones for learning among all youtube videos. keep your good work.
@TheMathCoach
3 жыл бұрын
Thanks a ton! There are a lot of great content creators on this platform :)
@ionutbum7799
4 жыл бұрын
Ty, dude. My teacher couldn't implement this into my head like this video did. Helpful!
@TheMathCoach
4 жыл бұрын
I don't blame him, Laurent Series is a tricky concept ^^
@NicolasSchmidMusic
4 жыл бұрын
You and faculty of khan are just the best in this topic. And your videos look pretty similar :)
@TheMathCoach
4 жыл бұрын
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.
@danielzhicool8048
10 ай бұрын
Thanks for this great video! Helped me a lot in preparing for the exam.
@TheMathCoach
7 ай бұрын
Hope it went well and you keep on learning!
@anushkachaturvedy3624
4 жыл бұрын
Thank you for this. I've been looking for these type of questions, and I found it here. Great explanation, easy breezy.
@TheMathCoach
4 жыл бұрын
I'm happy that to help!
@isabellacastellanosazuero9404
Жыл бұрын
Thank you so much for the help! It is by far the best video on this topic
@reubenwilliammpembe667
5 жыл бұрын
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
5 жыл бұрын
Happy to hear that you find my content useful and *best of luck* to you with your exam!
@溜溜梅-l4z
11 ай бұрын
THANKS!! Now I really understand why geometric series is so important!
@TheMathCoach
7 ай бұрын
Its is the real deal :)
@alcatraz5161
3 жыл бұрын
Beautifully explained Helped me out in the last throes of my complex analysis mandatory assignment : D Godspeed to you
@TheMathCoach
3 жыл бұрын
Wonderful! Happy to help :)
@zhikunli475
Жыл бұрын
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 KZitem 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 👍
@redgremlin2162
4 жыл бұрын
Extremely helpful man! Thanks!
@TheMathCoach
4 жыл бұрын
My pleasure :D
@nazaninghelichi5240
3 жыл бұрын
Life saving video! Amazing explanation and everything. Thanks man
@TheMathCoach
3 жыл бұрын
Happy to save lifes! Have a great day and best of luck with your studies :)
@mrpabloskyoskosky
4 жыл бұрын
Thank you for saving my life!
@TheMathCoach
3 жыл бұрын
I should reconsider going into the life saving bussiness!
@unplandsitch
3 жыл бұрын
After a lot of desperation you helped me so much, thanks!
@TheMathCoach
3 жыл бұрын
Glad you could leave the desparation behind you!
@rickpala_
4 жыл бұрын
this video saved my grade in complex analysis
@TheMathCoach
4 жыл бұрын
I'm glad I could help you with your grade :)
@physicsdepartmentuniversit8770
Жыл бұрын
your writing style is awesome
@TheMathCoach
Жыл бұрын
Thank you so much 😀 I have practiced it for a long long long time :D
@tarumpalo
4 жыл бұрын
Thank you. This helped me a lot and you are really great at explaining.
@TheMathCoach
4 жыл бұрын
I'm happy that you found it useful :)
@creweune7059
3 жыл бұрын
Thanks for the video, it is really helpful for this topic.
@TheMathCoach
3 жыл бұрын
Happy to help Crew! :)
@tombushell6581
2 жыл бұрын
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
2 жыл бұрын
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!
@chesterfielded
6 жыл бұрын
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
6 жыл бұрын
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 :)
@teriyaki8643
3 жыл бұрын
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
3 жыл бұрын
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 :)
@jokingseverus3221
6 жыл бұрын
Another awesome and helpful video to learn with a compact as well as attractive way of learning... thank you sir...
@TheMathCoach
6 жыл бұрын
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
6 жыл бұрын
TheMathCoach thank you sir... actually I am lucky that I find all that I need... next target is contour integration...😊
@TheMathCoach
6 жыл бұрын
Ops, forgot to reply here! Hope your contour integration reviewing went well :)
@willovecali_0208
4 ай бұрын
You save my exam tomorrow, THX
@TheMathCoach
3 ай бұрын
Hope your exam went well will :)
@haaniaaamir8297
6 жыл бұрын
Such an easy to follow and clear explanation!!
@TheMathCoach
6 жыл бұрын
I'm happy to help, glad you liked it :)
@SubrataGhanty
3 жыл бұрын
Amazing explanation... Love from 🇮🇳
@TheMathCoach
2 жыл бұрын
Glad to hear that you liked it! Love from swe
@ethiopiansickness
5 жыл бұрын
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
5 жыл бұрын
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!
@ethiopiansickness
5 жыл бұрын
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
5 жыл бұрын
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
5 жыл бұрын
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
5 жыл бұрын
Happy to help and good luck with your summer course, it sounds like a great decision to take early on :)
@IT--rz3br
5 жыл бұрын
very good video. Thank you so much . it really helped me to gain more profound knowledge about laurent series
@TheMathCoach
5 жыл бұрын
I'm happy to help!
@brandonk2465
5 жыл бұрын
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
5 жыл бұрын
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!
@ishraqueborshon
8 ай бұрын
Hey man, Great content! BTW may I know, what softwares and apps you used to make this video?
@TheMathCoach
7 ай бұрын
Hello, check out my channel! I have an video that goes through all the steps :)
@saradagunasekara2638
5 жыл бұрын
Thank you very much for the clear explanation... very much helpful
@TheMathCoach
5 жыл бұрын
I'm happy to help :)
@jeonghyeokim1017
3 жыл бұрын
This is so well done man im crying rn
@TheMathCoach
3 жыл бұрын
tears of joy I hope :)
@hamsalak9779
Жыл бұрын
holy mate that was some clean explanation. Tnx
@shingen911
7 жыл бұрын
Good timing! My exam is in two days :)
@TheMathCoach
7 жыл бұрын
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!
@bekiryufka
3 ай бұрын
just before exam! Thx a lot.
@TheMathCoach
3 ай бұрын
I hope you did well on the exam!
@deadawake123
6 жыл бұрын
Very clear with visual explanations, i like it! So how can I determine just by looking on the annulus (domain) if the serie in this specific annulus going to be Laurent or Taylor??
@TheMathCoach
6 жыл бұрын
Glad you liked it! I would recommend you to check out the next video (*Laurent Series and Taylor Series when to use which?*) in the playlist. Since I think that one might answer this question for you with the help of even more visual explanations compared to this video :) Let me know if it helped sort it out!
@deadawake123
6 жыл бұрын
@@TheMathCoach Exactly what I've needed for thanks a lot! Amazing explanation. Talented!
@TheMathCoach
6 жыл бұрын
I'm happy I could help and thanks for the kind words!
@Tiagogo21
5 жыл бұрын
Hello, thanks for the great video ! But something confuses me. for the last example where lzl > 2, you say that for the expansion of 1/z-1 we can use the same expansion as the one in the 1< lzl < 2 domain , I don't understand why ? Normally we must have the expansion of 1/z-1 valid for that last domain lzl>2 but here you write the expansion valid for lzl>1 ? Thanks !!
@TheMathCoach
5 жыл бұрын
First of I'm happy to hear that you liked the video! In the case with Laurent Series, we manipulate geometric series to get the correct kind of power series which are valid in the right domain. We already determined the principal part for the expression 1/(z-1) (timestamp 12:10) which is only defined where lzl > 1 (according to the formula for the second geometric series). In the last example, we are ones again looking for a principal part for the same expression 1/(z-1) and the only thing that is different from last time is the domain (lzl > 2) which it should be defined in. But we can still use it since lzl > 2 is a subset of lzl > 1 (which implies that the power series is also defined in this domain) and we can, therefore, save time in the last example and use the previously calculated expansion right from the start. I hope this cleared it up, let me know otherwise. Merry Christmas :)
@Tiagogo21
5 жыл бұрын
Yes !! I was so confused for a moment that I forgot that 2 was bigger than 1 and that it was still valid lol ! Thank you very much for the quick answer. Your videos really help me in my revisions for winter exams! Keep it up and Merry Christmas to you too !@@TheMathCoach
@AraDeanMaffy
7 жыл бұрын
Excellent, well done episode! ... congratulations again ;)
@TheMathCoach
7 жыл бұрын
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 :)
@arnaudleclef2021
4 жыл бұрын
Thank you for this video, it helped me a lot! :-)
@TheMathCoach
4 жыл бұрын
I'm happy to help!
@haneenmohamed5938
Ай бұрын
Thank you so much الله يجزيك خير ويهديك للحق، فهمتني الموضوع الصعب دا🤍🤍
@mokuscsik
3 жыл бұрын
Great stuff, thank you. Could I ask what software you use for your blackboard?
@TheMathCoach
3 жыл бұрын
Happy to hear that, I explain everything in detail in one of my videos: "How I make videos". You can find it on my channel :)
@mokuscsik
3 жыл бұрын
@@TheMathCoach Oh, I found it, thank you. Keep up the good work!
@MrKampfwurst
5 жыл бұрын
Great Explanation! Helped me a ton!
@TheMathCoach
5 жыл бұрын
I'm happy to hear that!
@fareedabifarraj483
3 жыл бұрын
Nice work! Can you please tell me how do you make a certain equation light up and everything else gets dim? What platform are you using?
@fareedabifarraj483
3 жыл бұрын
And is your handwriting so perfect? :p Or what font are you using?
@TheMathCoach
3 жыл бұрын
I used the highlight feature in Camtasia 9. You can see my whole process in my video "How I make Videos" on my channel :)
@fareedabifarraj483
3 жыл бұрын
@@TheMathCoach Thank you sooo muchh And Best of luck❤
@Higgsinophysics
5 жыл бұрын
Cyrstal clear. Thank you for sharing
@TheMathCoach
5 жыл бұрын
My pleasure!
@lmatton1
4 жыл бұрын
Excellent explanation- thank you!!
@TheMathCoach
4 жыл бұрын
I'm glad that you found it useful :)
@DrNMath
3 жыл бұрын
May I know the name of the software which you use please?
@TheMathCoach
3 жыл бұрын
Hello I made a video where I explains everything in details: kzitem.info/news/bejne/loZ90GWJoWZ9nmU , hope it helps and Happy Holidays!
@tubagusdaffaxi1216
9 ай бұрын
Thank you very much. You are the best
@TheMathCoach
7 ай бұрын
you are the best for wanting to learn!
@PhilTheViolinist
5 жыл бұрын
Great video. Liked and subscribed. I do have two questions though that would be great if you could answer for me. How do you go on to determine the Laurent Series expansion coefficients? Also, if a problem asks for "three term" expansion, does that mean the summation is from 0-2 instead of 0-infinity?
@TheMathCoach
5 жыл бұрын
Hello, happy you liked it. You can find the coefficients in two ways: 1) use the formula 00:45-00:55 in the video or 2) solve the Laurent Series expansion and look at the end result, lets say that your expansion ended up something like this f(z) = 1*(1/(z-1)^-3) + 2*(1/(z-1)^-2)+3*(1/(z-1)^-1) then you can see that the coefficients are the numbers before the term (1/(z-1)) so you would get that the coefficients are 1, 2 and 3. The value of n is equal to the name of the coefficient so the number 1 is equal to the coefficient n=-3. I have never heard of three-term expansion with Laurent series but my guess is that they want you to use the same principle as above but you are going to need to have *3* terms in your parentheses in the summation. So instead of finding an expression that looks like this: SUM (Term_1+Term_2)^n [Example SUM(2-z)^n] you are going to need to try and find something like this: SUM (Term_1+Term_2+Term_3) [Example SUM(1+1-z)^n] and then get the same result. This is just my guess though.
@tomatrix7525
3 жыл бұрын
Do you have any videos deriving the integral definition of the series?
@TheMathCoach
3 жыл бұрын
Are you referring to the Residue Theorem (en.wikipedia.org/wiki/Residue_theorem) that use the laruent series expression to determine the integral?
@wy2714
3 жыл бұрын
At 11:06 when you said add the two terms together, may i know why did you subtract instead?
@TheMathCoach
3 жыл бұрын
wrong use of words, I inserted the expressions for the fractions back into the formula above.
@aleksandrakedra1362
2 жыл бұрын
In the last one for |z|>2, shouldn't we solve it one more time for a=2 instead of using the previous one when we had a=1? Because now we're doing it for |z|>2, not |z|>1
@TheMathCoach
2 жыл бұрын
No need, if we have a geometric serie that is defined for IzI > 1 then it must also work for IzI > 2, since all of these complex numbers are contained inside of the circle that IzI > 1 creates.
@pranitashinde9228
4 жыл бұрын
Thank you sir for such an amazing lecture.
@TheMathCoach
4 жыл бұрын
Happy you liked it!
@euler0148
3 жыл бұрын
continue! you are a legend
@TheMathCoach
3 жыл бұрын
Happy to help! Next video coming out this Sunday :)
@euler0148
3 жыл бұрын
@@TheMathCoach thank you for that. happy new year
@TheMathCoach
3 жыл бұрын
@@euler0148 My pleasure, happy new year
@daniloup8139
4 жыл бұрын
Thank you very much, very helpful information 👍
@TheMathCoach
4 жыл бұрын
I'm just happy to help!
@praptikumarvishwakarmavvuc4608
Жыл бұрын
NIce Explanation. Thank You
@TheMathCoach
Жыл бұрын
Glad it was helpful!
@Alabdullelah
5 жыл бұрын
WOW!!! You literally made my day . THANK YOU SSSSOOOO MUCH! 8) Just quick question on the second question, why did we have 1
@TheMathCoach
5 жыл бұрын
Happy to help :) The boundaries you are referring to are corresponding to the circle we drew at 08:10 |z-1| = 1 (radius 1 and centered at z=1. The formula for a circle is |z-z_center| = radius) and if we had used 2 instead of 1 then it would not have been the same circle, the center of the circle would have been the same but not the radius and the circle would not intersect with the pole at z=2 as we want.
@jonaargueta771
5 жыл бұрын
This video is exactly what we wanted
@TheMathCoach
5 жыл бұрын
That is great to hear, happy to help!
@jamestanaka686
4 жыл бұрын
How do I find the Laurent or Taylor series for 1/sqrt(1+z) ...? Please help .... It seems I cannot use geometric series.
@TheMathCoach
4 жыл бұрын
What have you done so far?
@jamestanaka686
4 жыл бұрын
@@TheMathCoach In fact, I used binomial series formula to easily solve. Another solution I can think of is to take derivative many times to find the pattern and plug into the taylor series formula.
@armchair8258
6 жыл бұрын
You explain so well, thanks!!
@TheMathCoach
6 жыл бұрын
No problem, I'm glad you liked it :)
@rfy8463
6 жыл бұрын
Hi how to find the principal part of the Laurent series expansion of f(z)= (sinh z)/[(z^2)(z-2)^2] around z = 2. my attempt: (sinh 2)/ [4(z-2)^2]. is this correct?
@TheMathCoach
6 жыл бұрын
Hello, it seems that you are really close to the correct answer! :) I seems like you have managed to obtain the coefficient in front of (z-2)^-2, which is the highest negative power term, so that is nice! But remember that the principal part is ALL the terms with negative power, so you also have to include the coefficient in front of (z-2)^-1 aswell in your final answer. This is probably just some minor error, could you present your calculations in more details and we might be able to correct it together :) Best regards,
@rfy8463
6 жыл бұрын
Hello, Thank you for such a prompt reply! :) f(z)= (sinh z)/[(z^2)(z-2)^2] around z = 2. below is my working in details, (please pinpoint if there is any mistake in my explanation/calculation) since the singularity of f(z) at z=2 and the centre of the circle coincide, hence in this case I don't need to find the expansion of 1/(z-2)^2 a. 1/(z-2)^2 b. my expansion for sinh (z) = (sinh(2) + (z-2)cosh(2) + (1/2)(Sinh 2)(z-2)^2 + .... c. my expansion for 1/z^2 as we're expanding around point 2, 1/z^2 = {1/[(z-2)+2]}^2 (after doing the manipulation and then using the geometric expansion) = [(1/4) - (z-2)/4 + [(3)(z-2)^2]/16 - .... therefore, f(z) = (a)(b)(c) [1/(z-2)^2] [(sinh(2) + (z-2)cosh(2) + (1/2)(Sinh 2)(z-2)^2 + ....] [(1/4) - (z-2)/4 + [(3)(z-2)^2]/16 - .... ] (sinh 2) / [4(z-2)^2] - [(z-2)cosh(2)(z-2)/(z-2)^2] + .... (hence the (z-2) cancels out in the 2nd term,) so the only principal part we have (sinh 2) / [4(z-2)^2]
@TheMathCoach
6 жыл бұрын
You got the theory right, all the statements *a* , *b* and *c* are correct statements! Try to do the last calculation one more time (really take the time) and you will see that you will get it right, since you should be able to get two terms with negative power by the combination of the factor (1/4) from *c* , the first two factors in *b* and the 1/(z-2)^2 in *a* . I double checked your calculations in wolfram and you will be able to get the correct answer with your statements, so good job :)
@rfy8463
6 жыл бұрын
OHHHH yes yes, ok that was such a silly mistake :'D thank you, man! you are amazing, I learnt a lot from your channel! :) keep it up. also thank you for your time verifying my work :)
@TheMathCoach
6 жыл бұрын
I'm happy to help! Also thanks for the kind words, glad that my content can be useful for some people. Good luck with the rest of your studies :)
@ahmadjafararifi5575
5 жыл бұрын
it's a clear explanation, very helpful.
@TheMathCoach
5 жыл бұрын
Happy you liked it.
@frechernono6401
4 жыл бұрын
Really well expleained! Thank you
@TheMathCoach
4 жыл бұрын
Happy to help!
@xyz111xyz
Жыл бұрын
thank you very much, finally know what's going on with R,r :D
@TheMathCoach
Жыл бұрын
Happy to help out! Sometimes an image is all one needs ^^
@shaun4.
2 жыл бұрын
Great lesson!
@TheMathCoach
2 жыл бұрын
Glad you liked it!
@osamazahid715
6 жыл бұрын
which software are you using for making this lecture
@TheMathCoach
6 жыл бұрын
Adobe Photoshop for the writing and then I record my screen with Camtasia, which is also my editing program. The audio is later recorded over the video by using Audacity and then I match the video and audio files with Camtasia :)
@racionalizando4313
4 жыл бұрын
Sir. you would make an video to explain locus of complex numbers, hyperbola, circle, parabole , co-ordenate geometry?
@TheMathCoach
4 жыл бұрын
No plans for that right now.
@racionalizando4313
4 жыл бұрын
@@TheMathCoach Ok! :(
@johannatholen6168
6 жыл бұрын
Do you mind making a video for the proof aswell? I can't seem to find any video for the proof.
@TheMathCoach
6 жыл бұрын
I'm leaving for a longer period of time in like 5 hours so I don't have the time necessary to make this kind of video right away since it is *quite* long. I will have your suggestion in mind for further videos but I can't make any promises. But if you want to understand it right away and don't mind seeing the proof in *writing* form then you can read about it on page 269 - 273 in english-c.tongji.edu.cn/_SiteConf/files/2014/05/05/file_53676237d7159.pdf (Saff & Snider, Fundamentals of complex analysis, with applications 2003). This book is actually the same book I used when I took the course. Hope it helps!
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