Your videos are literally gold and saving me from a class where this whole part was completely glossed over. You are also great and explaining and providing thorough examples!
Taking my methods of theoretical physics exam on the 6th June. You don't even understand how much these videos are going to bring my mark up! Fantastic, thank you so much.
Happy to be able to help and just shoot me a question in the comments if you want any clarification about the content in the videos. Best of luck with your exam :)
To look at a series and figure out whether or not it converges, you use the ratio test. First, calculate the modulus (absolute value) of the a(n+1)th term divided by the a(n)th term. In this example, that would be the modulus of (-1)^(n+1) x z^(n+1) / 2^(n+1+1) divided by (-1)^n x z^n / 2^(n+1) which gives the modulus of (-1) x z/2 as can be seen in the video (which is of course just z/2). The next step is to take the limit as n tends to infinity, but there are no terms dependant on n, and so nothing changes. Then, there are three possibilities for the series. If the fraction we calculated is less than 1, the series converges. If it is more than 1, the series diverges. Finally, if it is equal to 1 then the test is inconclusive and other tests are required to determine whether the series converges. Google the ratio test, its a standard formula. Hope that helps
I think that Katherine's reply summed it up well. But in short, I know that the formula (1) is valid (that series will be convergent for all w-values that satfies that condition) and now I have simply used that formula with w = -z/2, hence I know that the sum will be valid.
@@OldDewGaming I'm really happy that you find my content useful! I must first finish my complex analysis playlist first and then I might continue with differential equations (all the different transforms etc.), Groups and Rings or something else, since I have not decided yet, but I will take this into consideration when doing that. I can't promise anything right now but thanks for the suggestions :)
This series of Complex Analysis videos is one of the best on Yt !! and Ive watched a lot. Sadly, I can only give you one thumb up. I wonder why you didnt cover Laurent - Series ? Again - superb videos ! thanks a lot ! ( Follow up Question : How can one quickly determine the Taylorseries outside a disk region already knowing the Taylor series inside the disk region ? )
Thank you very much for the kind words and thanks for the "thumb up", all form of support is equally appreciated! I'm just glad that this series can be of us for people that would like to learn more about the subject :) For the first question: My plan is to cover the subject "Power Series" in complex analysis by making three videos. The first one is about Taylor Series (this video), the second one will be about Laurent Series and the third one will be about the difference between Laurent Series and Taylor Series. The third video will cover how to determine which on to use when you want to determine a Power Series for a function, since I think this a problematic thing to understand. I'm currently working on the second video about Laurent Series and the reason I split them up into three videos is that I don't like videos to be up to 30-40 mins long. Great second question, the thing is that the Taylor Series for a function f(z) around some point z_0 is unique and therefore the Taylor Series around z_0 will be the same in the whole comples plane. So if you find the Taylor Series inside a disk region then it will be the same outside the region aswell. BUT this Taylor Series will only be equal to the function f(z) inside the region which is determined by the radius of convergence. Are you satisfied with those answer? Just let me know if you would like us to discuss it more. I would like to ask you one thing, do you think the videos speed is good and do you like the Content Screen in the start of the video, when I show everything the video will cover? Again thanks so much for watching and asking questions, this is stuff that really makes me happy, to be able to help and consider subscribing if you would like to know the moment I release my next video about Laurent Series! Best regards, TheMathCoach ^^
You obviously put a lot of thought in your videos before you release them ! since you do your videos well prepared you dont bore your viewers time by putting down equations - biggest mistake most math channels do. Instead of wasting time while putting down everything ( this is why students easily lose focus- one should only put down parts of the equation which are key) . Most of the writing can be done before starting the video - this shortens the video immense. -- since you asked: I usually watch videos already knowing a lot about the topic, so people like me can change the speed in the settings !! meaning you you shouldnt change a thing you already are doing a superb job ! thumb up !
Hello, you can, for example, use the trick shown in the video at 5:40 and look at your function as the derivative of another function and solve it for this primitive function. Another way is to use partial fractions as is shown at 7:00 to break it up into two expressions that can be solved separately.
@@der_schutzer9521 No actually, why do you add a +1 to the exponent? Edit: Actually, nvm figured it out. For those wondering, it's the factor outside the sigma sign, didn't notice that one, in fact, didn't account those for a whole series of examples where theres an outside factor.
@@inthebackwiththerabbish I dont solve viewer example questions (it would never end if i started) instead I try to give them the methods (the theory in the video) so they hopefully will be able to solve it themselves. otherwise if a viewer contact me with details regarding the steps they have taken and theirs though-process THEN I can help out and give them some direction (because they already did some work and tried) but not them they only want the answer.
@@TheMathCoach Thanks so much for your response (forgot to say it but you've helped me a lot with your videos). With respect to the physics questions i was looking for something like your videos :o like some real teaching with examples, graphs and stuff like that.
Sir can you upload videos regarding the topics like identity theorem, schwarz lemma, meromorphic functions and its applications in complex analysis, if you do then it will be very helpful.
Hello, my plan with this playlist is a work in progress and thank you so much for the suggestions, I will keep them in mind for upcomming videos. I have announced that I'm going to cover Annalytic Continuation and I should be able to include the identify theorem in that video, hurray! I might be able to do separate videos about meromorphic functions and schwarz lemma, I will have to look that one up in more detail and see if I got the time (Master Thesis coming up). But just to let you know, it can take some time before I can start working with these videos since I'm right now focusing on Power Series, Conformal mappings and after that I will probably do some Integral Calculations to wrap up the most important parts of Complex analysis. Best regards,
Absolutely, I will try to help you to the best of my ability. You can write here in this thread or contact me on Twitter (@The_MathCoach), w/e suits you the most.
I presume you are referring to your latest comment from "Zeros and Poles", thanks for the follow up answer. I will consider including a introduction video to the playlist, about the practical uses of the subjects presented in this playlist after it is completely done. I will however unlikely change my format for the upcoming videos in this playlist, since they are quite long as they are and I like to focus on the things you need to know to be able to pass an exam in a traditional course, even though the concepts has a big range of practical use. This is since I think that my viewers will be able to access the practical uses of the concepts from other sources and I like to be consistent throughout the playlist. Thanks for the suggestion! :)
@@TheMathCoach Your concise and direct method is what makes your videos standout. Please keep up the good work. Many thanks for taking the time to make this video.
Your videos are literally gold and saving me from a class where this whole part was completely glossed over. You are also great and explaining and providing thorough examples!
I'm happy to hear that I can help you out and thanks for the feedback :)
Taking my methods of theoretical physics exam on the 6th June. You don't even understand how much these videos are going to bring my mark up! Fantastic, thank you so much.
Happy to be able to help and just shoot me a question in the comments if you want any clarification about the content in the videos. Best of luck with your exam :)
Wow, this is pure gold. Thanks for uploading, it is perfect for revision before an exam.
Thank you so much for the kind words, I'm glad that you found it useful :)
Just in time when i'm studying complex analysis. Thank god and thank you so so much for this video. It helps me a LOT.
Happy to help! Best of luck with your exam :)
Another phenomenal video, and I am thinking of just watching 1-2 more before I go to sleep. But, I will be right back here tomorrow!
"Just one more youtube video" looks at clock 5 AM, damn it! Happy to see you binging the content!
At 4:10 How do you know the series is convergent when |-z/2|
To look at a series and figure out whether or not it converges, you use the ratio test. First, calculate the modulus (absolute value) of the a(n+1)th term divided by the a(n)th term. In this example, that would be the modulus of (-1)^(n+1) x z^(n+1) / 2^(n+1+1) divided by (-1)^n x z^n / 2^(n+1) which gives the modulus of (-1) x z/2 as can be seen in the video (which is of course just z/2). The next step is to take the limit as n tends to infinity, but there are no terms dependant on n, and so nothing changes. Then, there are three possibilities for the series. If the fraction we calculated is less than 1, the series converges. If it is more than 1, the series diverges. Finally, if it is equal to 1 then the test is inconclusive and other tests are required to determine whether the series converges. Google the ratio test, its a standard formula. Hope that helps
I think that Katherine's reply summed it up well. But in short, I know that the formula (1) is valid (that series will be convergent for all w-values that satfies that condition) and now I have simply used that formula with w = -z/2, hence I know that the sum will be valid.
@@KatherineRenshaw got it! thank you .
@@TheMathCoach yup. thanks!
learning this stuff a day before my exam lol, beyond grateful!!
Happy to help and I hope you did well on your exam!
You explain really good! You can make a career out of this!
Thank you, I'm happy to help and I will come back to making more videos eventually :)
@@TheMathCoach You really are an amazing teacher! Could you make some videos on Z, Fourier, and Laplace transform theories?
@@OldDewGaming I'm really happy that you find my content useful! I must first finish my complex analysis playlist first and then I might continue with differential equations (all the different transforms etc.), Groups and Rings or something else, since I have not decided yet, but I will take this into consideration when doing that.
I can't promise anything right now but thanks for the suggestions :)
@@TheMathCoach Thank you for your quick response! All the best!
you are a true savior, thank you!
You're welcome!
Your method of explaining and presenting is extraordinary.....upload more and more vidoes...even on basics of topics...it helps...
Thank you for the kind words, I will try to get back to uploading eventually!
The Lectures are amazing thank you sir! However, hasn't someone commented about his handwriting yet?
My pleasure to be able to help and I actually think you are the first one!
Thank you very much and may the force be with you!
and thank you, good sir ^^
Thank you so much, your videos are very helpful and your voice is so gentle so it makes focusing on the subject easier.=)
I'm just glad it did not make you go to sleep completly :)
Thank you for your time that you spent on this video , very helpful.
Thank you for the kind words, I'm just happy that it could be useful to others :)
This series of Complex Analysis videos is one of the best on Yt !! and Ive watched a lot. Sadly, I can only give you one thumb up. I wonder why you didnt cover Laurent - Series ? Again - superb videos ! thanks a lot ! ( Follow up Question : How can one quickly determine the Taylorseries outside a disk region already knowing the Taylor series inside the disk region ? )
Thank you very much for the kind words and thanks for the "thumb up", all form of support is equally appreciated! I'm just glad that this series can be of us for people that would like to learn more about the subject :)
For the first question: My plan is to cover the subject "Power Series" in complex analysis by making three videos. The first one is about Taylor Series (this video), the second one will be about Laurent Series and the third one will be about the difference between Laurent Series and Taylor Series. The third video will cover how to determine which on to use when you want to determine a Power Series for a function, since I think this a problematic thing to understand. I'm currently working on the second video about Laurent Series and the reason I split them up into three videos is that I don't like videos to be up to 30-40 mins long.
Great second question, the thing is that the Taylor Series for a function f(z) around some point z_0 is unique and therefore the Taylor Series around z_0 will be the same in the whole comples plane. So if you find the Taylor Series inside a disk region then it will be the same outside the region aswell. BUT this Taylor Series will only be equal to the function f(z) inside the region which is determined by the radius of convergence.
Are you satisfied with those answer? Just let me know if you would like us to discuss it more.
I would like to ask you one thing, do you think the videos speed is good and do you like the Content Screen in the start of the video, when I show everything the video will cover? Again thanks so much for watching and asking questions, this is stuff that really makes me happy, to be able to help and consider subscribing if you would like to know the moment I release my next video about Laurent Series!
Best regards, TheMathCoach ^^
You obviously put a lot of thought in your videos before you release them ! since you do your videos well prepared you dont bore your viewers time by putting down equations - biggest mistake most math channels do. Instead of wasting time while putting down everything ( this is why students easily lose focus- one should only put down parts of the equation which are key) . Most of the writing can be done before starting the video - this shortens the video immense. -- since you asked: I usually watch videos already knowing a lot about the topic, so people like me can change the speed in the settings !! meaning you you shouldnt change a thing you already are doing a superb job ! thumb up !
Awesome, thanks a lot for the feedback and have a lovely day now!
I can't download because its saying you don't have access.
Test again now, I just accepted all the requests.
I'm just portuguese man , but I love this Chanel
this swede bid you welcome to the channel!
How would we expand 1/(1+z)'2...it confuses me when we have the entire expression squared
Hello, you can, for example, use the trick shown in the video at 5:40 and look at your function as the derivative of another function and solve it for this primitive function. Another way is to use partial fractions as is shown at 7:00 to break it up into two expressions that can be solved separately.
@@TheMathCoach Thank you so much! You truly are a lifesaver❤️
If a function has no singularities, then it’s radius of convergence would be all of the complex plane ??
yes and this function is entire.
It is as Jing Gong said below, it will be for the whole complex plan :)
Amazing video!
Amazing video! I understood all! Just a doubt: (z/2)^n is z^n/2^(n+1) ?? Why add +1 to the 2's exponent?
Glad you liked it and that does not seem right. Could you give me the timestamp and I will look into it :)
No actually the video is right, I see the reason now I feel stupid lol thank you again!!
Don't be, the most important thing is that we got it right in the end, happy we could solve it so easily :)
@@der_schutzer9521 No actually, why do you add a +1 to the exponent?
Edit: Actually, nvm figured it out. For those wondering, it's the factor outside the sigma sign, didn't notice that one, in fact, didn't account those for a whole series of examples where theres an outside factor.
Hello, what about f(z)= z/log (z+1) around z=0? I couldn't find an answer!! Would you help me, please?
Hello, no sorry but I hope you solved it in the end.
@@TheMathCoachwhy wouldn’t you help?
@@inthebackwiththerabbish I dont solve viewer example questions (it would never end if i started) instead I try to give them the methods (the theory in the video) so they hopefully will be able to solve it themselves.
otherwise if a viewer contact me with details regarding the steps they have taken and theirs though-process THEN I can help out and give them some direction (because they already did some work and tried) but not them they only want the answer.
@@TheMathCoach W for responding. And I got you that makes a lof of sense
@@inthebackwiththerabbish thank you, I always try to responed to all comments, sometimes it just take some more time for me to get to it :)
Very nice video love your content keep it up c:
Well question out of context. Anyone knows of some good physics channel(as good as this one to learn)?
Glad you liked it :)
Not sure which level you are looking for but I myself like: Veratasium, Crash Course and MinutePhysics for starters.
@@TheMathCoach Thanks so much for your response (forgot to say it but you've helped me a lot with your videos). With respect to the physics questions i was looking for something like your videos :o like some real teaching with examples, graphs and stuff like that.
Sir can you upload videos regarding the topics like identity theorem, schwarz lemma, meromorphic functions and its applications in complex analysis, if you do then it will be very helpful.
Hello, my plan with this playlist is a work in progress and thank you so much for the suggestions, I will keep them in mind for upcomming videos.
I have announced that I'm going to cover Annalytic Continuation and I should be able to include the identify theorem in that video, hurray! I might be able to do separate videos about meromorphic functions and schwarz lemma, I will have to look that one up in more detail and see if I got the time (Master Thesis coming up).
But just to let you know, it can take some time before I can start working with these videos since I'm right now focusing on Power Series, Conformal mappings and after that I will probably do some Integral Calculations to wrap up the most important parts of Complex analysis.
Best regards,
okk...looking forward for your videos. Thank you.
No problem, I'm glad you are enjoying them!
Have a great day now :)
If I have problems regarding those topics can I inform you?
Absolutely, I will try to help you to the best of my ability.
You can write here in this thread or contact me on Twitter (@The_MathCoach), w/e suits you the most.
Super good video
a super good video and now with another great comment!
good explanation, thanks
I'm happy to help!
THANK YOU
really helpful thanks
My pleasure!
Beautiful
Happy you liked it!
i love you
and I love you too, internet stranger!
just blah.. make it practical... just see Don't Memorize you tube videos on complex numbers.... please make it ur lectures like that....
I presume you are referring to your latest comment from "Zeros and Poles", thanks for the follow up answer. I will consider including a introduction video to the playlist, about the practical uses of the subjects presented in this playlist after it is completely done.
I will however unlikely change my format for the upcoming videos in this playlist, since they are quite long as they are and I like to focus on the things you need to know to be able to pass an exam in a traditional course, even though the concepts has a big range of practical use. This is since I think that my viewers will be able to access the practical uses of the concepts from other sources and I like to be consistent throughout the playlist.
Thanks for the suggestion! :)
@@TheMathCoach Your concise and direct method is what makes your videos standout. Please keep up the good work. Many thanks for taking the time to make this video.