Laurent Series Explained | How to Determine Laurent Series | Complex Analysis #9
Everything you need to know about Laurent Series explained. The video will contain problems on Laurent Series and how to solve them all for each Laurent Series.
The video will include concepts as:
► Definition of Laurent Series
► Principal part and Analytic part of a Laurent Series
► Convergence of the Principal part and Analytic part
► A theorem about when we can use Laurent Series
► How to determine all possible Laurent Series around some point of expansion
► How to solve Laurent Series.
LINK TO COMPLEX ANALYSIS PLAYLIST
• The Complete Guide to ...
LINK TO CANVAS
drive.google.com/file/d/1IHef...
SUPPORT
Consider subscribing, liking or leaving a comment, if you enjoyed the video or if it helped you understand the subject. It really helps me a lot.
CLARIFICATION OF THE METHOD:
To determine all possible Laurent Series:
Start by marking the important points on the graph, the important points are the poles of the function and the point of expansion. The will divide the complex plan into several domains and each of these domains will have its own Laurent Series, since none of these domain will contain any poles of the function.
You may note that most of the time we only need to determine ONE of the parts (analytic or principal part) to determine the Laurent Series. This comes from the fact that both of these parts are only present (converges) if we are inside an annulus domain. If you want to determine a Laurent Series outside of a circle then you only need the principal part (since the analytic part will not converge in this domain) and if you want to determine the Laurent Series inside of a circle then you only need the Analytic part (since the principal part will not converge in this domain).
CONCEPTS FROM THE VIDEO
► Laurent Series
A Laurent Series is a specific kind of power series and is used to approximate an analytic function f(z) around some point z_0 (note that z_0 can be an isolated singularity) in the complex plane
... + (a_-3) *(z-z_0)^-3 + (a_-2) *(z-z_0)^-2 + (a_-1) *(z-z_0)^-1 + a_0 + a_1 *(z-z_0) + a_2 *(z-z_0)^2 + a_3 *(z-z_0)^3 + ...
where the coefficients a_n are determined by contour integration, but 99,9 % of the cases these are determined by geometric series. Note that: "... + (a_-3) *(z-z_0)^-3 + (a_-2) *(z-z_0)^-2" is called the principal part, while "a_0 + a_1 *(z-z_0) + a_2 *(z-z_0)^2 + a_3 *(z-z_0)^3 + ..." is called the analytic part.
►Geometric Series
A geometric series is a series with a constant ratio between successive terms. An example on a geometric series is
1/(1-w) = w^0 + w^1 + w^2 +... for abs(w) smaller than 1
which can be modified to the following
1/(1- 1/w) = (1/w)^0 + (1/w)^1 + (1/w)^2 +... for abs(w) bigger than 1
and the reason these two series are used a lot to solve these kind of problems, is because this geometric series looks pretty much like the Laurent Series we would like to obtain.
► Poles
A pole is a specific kind of singularity, the short and the most intuitive definition is that poles are points z_0 in the complex plane so that f(z_0) = g(z_0)/0, where g(z_0) =\= 0.
► Partial Fraction
The partial fraction decomposition or partial fraction expansion of a rational function is used to express the fraction as a sum of fractions with a simpler denominator.
[Link to video is coming].
TIMESTAMPS
00:00 Intro
00:13 Theorem Laurent Series
01:06 What is an Annulus domain
02:04 Good things to know
03:40 Why geometric series are the best
Examples: Determine all possible Laurent Series for the following functions
05:20 f(z) = 1/(z-2) around z=0
08:02 f(z) = 1/(z-2) around z=1
09:48 f(z) = 1/((z-1)(z-2)) around z=0
SOCIAL
► Follow me on KZread: bit.ly/1NQhPJ9
► Follow me on Twitter: / the_mathcoach
SOURCES:
Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics: Pearson New International Edition.
mathworld.wolfram.com/LaurentS...
en.wikipedia.org/wiki/Laurent...
sym.lboro.ac.uk/resources/Hand...
zimmer.csufresno.edu/~doreendl...
www.math.ust.hk/~maykwok/cour...
HASHTAGS
#TheMathCoach #ComplexAnalysis #Complex Analysis Playlist
Пікірлер: 356
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: kzread.info/head/PLraTC6fSWOiptqOd_rMhFk6mZM30l7SqQ
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...
By far the best explanation of laurent series on you tube. thanks for help!
@TheMathCoach
5 жыл бұрын
Happy to help and thank you for your kind words, much appreciated!
@georgeyu7987
4 жыл бұрын
agree
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!
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 :)
You can't imagine how much I love you rn, you saved my complex analysis course xd
@TheMathCoach
4 жыл бұрын
Happy to help!
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
2 жыл бұрын
thank you my dear king, i really appreciate it!
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 :)
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
4 жыл бұрын
Thank you for the kind words :D Glad that my content is useful for you!
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
5 жыл бұрын
I'm happy you liked it, thanks for the kind words :) I'm planning to one day continue!
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 :)
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 :)
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!
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 :)
This is absolutely amazing. Thank you so much!
@TheMathCoach
6 жыл бұрын
I'm glad you liked it! :)
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 :)
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 :)
Thank you so much for the help! It is by far the best video on this topic
You save lives with videos like these
loved it ! excellent and crispy explanation ...just to the point...keep going students like me needs teacher like you 📝🙌
@TheMathCoach
5 жыл бұрын
Ohh lovely! Happy to help and also glad that you found my format and content useful :D
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!
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 (kzread.info/dash/bejne/gn6F1LZ8Yc3QlZM.html) 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 :)
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 :)
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!
Thankyou so much sir, I searched alot , this is the only video available for this concept.
@TheMathCoach
3 ай бұрын
Happy to help out, I also like my video about Laurent Series, one of my favorites!
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 :)
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 ^^
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 :)
Best elaboration of Laurent Series ever seen!
@TheMathCoach
4 ай бұрын
Happy to be able to help!
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 :)
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 :)
Such an easy to follow and clear explanation!!
@TheMathCoach
6 жыл бұрын
I'm happy to help, glad you liked it :)
After a lot of desperation you helped me so much, thanks!
@TheMathCoach
3 жыл бұрын
Glad you could leave the desparation behind you!
Exam in 5 days, keen for this playlist!
@TheMathCoach
6 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
3 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)
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.
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
Best explanation of Laurent Series on youtube..
@TheMathCoach
10 ай бұрын
Glad you think so! I'm happy to help out and bring more ways for people to understand the subject :)
Extremely helpful man! Thanks!
@TheMathCoach
4 жыл бұрын
My pleasure :D
Thanks for this great video! Helped me a lot in preparing for the exam.
@TheMathCoach
4 ай бұрын
Hope it went well and you keep on learning!
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?
Thank you very much for the clear explanation... very much helpful
@TheMathCoach
4 жыл бұрын
I'm happy to help :)
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 :)
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!
Thanks for the video, it is really helpful for this topic.
@TheMathCoach
3 жыл бұрын
Happy to help Crew! :)
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 :)
Thank you for this video, it helped me a lot! :-)
@TheMathCoach
4 жыл бұрын
I'm happy to help!
you should have a million followers o more, this was a really good explanation , you rock!!!!
@TheMathCoach
10 ай бұрын
thank you for the kind words, it warms me up! :)
You and faculty of khan are just the best in this topic. And your videos look pretty similar :)
@TheMathCoach
3 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.
holy mate that was some clean explanation. Tnx
You explain so well, thanks!!
@TheMathCoach
5 жыл бұрын
No problem, I'm glad you liked it :)
Great Explanation! Helped me a ton!
@TheMathCoach
5 жыл бұрын
I'm happy to hear that!
Excellent, well done episode! ... congratulations again ;)
@TheMathCoach
6 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 :)
Thank you for saving my life!
@TheMathCoach
3 жыл бұрын
I should reconsider going into the life saving bussiness!
THANKS!! Now I really understand why geometric series is so important!
@TheMathCoach
3 ай бұрын
Its is the real deal :)
Thank you sir for such an amazing lecture.
@TheMathCoach
4 жыл бұрын
Happy you liked it!
Cyrstal clear. Thank you for sharing
@TheMathCoach
5 жыл бұрын
My pleasure!
Excellent explanation- thank you!!
@TheMathCoach
4 жыл бұрын
I'm glad that you found it useful :)
Thank you very much, very helpful information 👍
@TheMathCoach
4 жыл бұрын
I'm just happy to help!
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 :)
Thank you very much. You are the best
@TheMathCoach
4 ай бұрын
you are the best for wanting to learn!
it's a clear explanation, very helpful.
@TheMathCoach
5 жыл бұрын
Happy you liked it.
Awesome explanation, thanks.
@TheMathCoach
6 жыл бұрын
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!
This is so well done man im crying rn
@TheMathCoach
3 жыл бұрын
tears of joy I hope :)
NIce Explanation. Thank You
@TheMathCoach
10 ай бұрын
Glad it was helpful!
You save my exam tomorrow, THX
Thank you so much for helping out
@TheMathCoach
4 жыл бұрын
Happy to help!
Great video, thanks!
@TheMathCoach
4 жыл бұрын
My pleasure to help!
This has saved me. My thanks.
@TheMathCoach
4 жыл бұрын
I'm happy to help :)
Great lesson!
@TheMathCoach
2 жыл бұрын
Glad you liked it!
Amazing explanation... Love from 🇮🇳
@TheMathCoach
2 жыл бұрын
Glad to hear that you liked it! Love from swe
Thank you sir...
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 KZread 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 👍
Thank you so much my friend👍👍👍
@TheMathCoach
4 жыл бұрын
I'm just happy to help!
thank you very much, finally know what's going on with R,r :D
@TheMathCoach
10 ай бұрын
Happy to help out! Sometimes an image is all one needs ^^
Good timing! My exam is in two days :)
@TheMathCoach
6 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!
it's is help full video thanks a lot!
@TheMathCoach
2 жыл бұрын
Glad it helped!
best explanation of laurent sweries of expansion.cudoz
@TheMathCoach
5 жыл бұрын
Happy to help. Thanks for the kind words :)
great video , very clear
@TheMathCoach
2 жыл бұрын
Glad it was helpful!
this video saved my grade in complex analysis
@TheMathCoach
4 жыл бұрын
I'm glad I could help you with your grade :)
Thank you again!
@TheMathCoach
10 ай бұрын
Any time!
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 :)
your writing style is awesome
@TheMathCoach
10 ай бұрын
Thank you so much 😀 I have practiced it for a long long long time :D
great video.. thanks a lot
@TheMathCoach
2 жыл бұрын
Glad you liked it!
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.
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
4 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!
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!
Thanks You're Amazing
@TheMathCoach
2 жыл бұрын
Happy to be able to help out!
thanks for making this vdo!
@TheMathCoach
3 жыл бұрын
Happy to help!
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
quality explanation! Thnx
@TheMathCoach
4 жыл бұрын
No problem, I'm happy to help :)
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
4 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.
This was great!
@TheMathCoach
4 жыл бұрын
Glad you liked it ^^
Excellent video.
@TheMathCoach
5 жыл бұрын
which now have one more excellent comment. Happy you liked it!
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
5 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
5 жыл бұрын
@@TheMathCoach Exactly what I've needed for thanks a lot! Amazing explanation. Talented!
@TheMathCoach
5 жыл бұрын
I'm happy I could help and thanks for the kind words!
wow...found just what i needed
@TheMathCoach
2 жыл бұрын
sometime you got to be lucky :D
Thank u so much!
@TheMathCoach
4 жыл бұрын
I'm just happy to help :)
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!
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
6 жыл бұрын
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!
thanks man......
@TheMathCoach
2 жыл бұрын
No problem mate.....
I understood one thing really well and that is Laurent series is hard as hell.
@TheMathCoach
2 жыл бұрын
Glad you took away something from the video :)