Convergent is dual to divergent -- power series are dual! Syntropy is dual to increasing entropy --the 4th law of thermodynamics! Analysis or wholes become parts is an entropic process or reductionist process -- divergent. Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent. Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. "Always two there are" -- Yoda.
Thank you so much for making these videos. I'm a physics student, and these concepts aren't taught this well. Also, your handwriting is so neat! love from Palestine
Convergent is dual to divergent -- power series are dual! Syntropy is dual to increasing entropy --the 4th law of thermodynamics! Analysis or wholes become parts is an entropic process or reductionist process -- divergent. Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent. Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. "Always two there are" -- Yoda.
00:00 Intro 0:57 Why power series are important? Example of exp(z) 2:05 General definition for C 4:03 Example. Geometric series + conditions for convergence 9:06 Cauchy-Hadamard theorem
Convergent is dual to divergent -- power series are dual! Syntropy is dual to increasing entropy --the 4th law of thermodynamics! Analysis or wholes become parts is an entropic process or reductionist process -- divergent. Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent. Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. "Always two there are" -- Yoda.
Convergent is dual to divergent -- power series are dual! Syntropy is dual to increasing entropy --the 4th law of thermodynamics! Analysis or wholes become parts is an entropic process or reductionist process -- divergent. Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent. Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. "Always two there are" -- Yoda.
Hey! Fantastic video, really well-made and comprehensive, and easy to understand as well. I have one request tho, if possible please include proofs of the theorems you mention (such as Cauchy Hadamard, or that power series converge in a ball), or at least provide some links for the same. Much appreciated, thanks!
I have a friend that is studying abroad in Germany and when he showed me the Cauchy-Hadamard limit I was kinda confused because we use the d'Alembert rule and it seems to be a lot simpler. Any reason why to use C-H over it?
@@brightsideofmaths thank you very much! I am an aspiring teacher and your videos have helped me organise so much. If you have time and are intested, I would love to see your work process for these videos, they are incredible!
@@brightsideofmaths Convergent is dual to divergent -- power series are dual! Syntropy is dual to increasing entropy --the 4th law of thermodynamics! Analysis or wholes become parts is an entropic process or reductionist process -- divergent. Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent. Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. "Always two there are" -- Yoda. Energy is duality, duality is energy Everything in physics is made from energy including mathematics!
Convergent is dual to divergent -- power series are dual! Syntropy is dual to increasing entropy --the 4th law of thermodynamics! Analysis or wholes become parts is an entropic process or reductionist process -- divergent. Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent. Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant. "Always two there are" -- Yoda.
I always stay anxious for next video of this channel. These videos are true Math classes.
Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.
Thank you so much for making these videos. I'm a physics student, and these concepts aren't taught this well.
Also, your handwriting is so neat!
love from Palestine
Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.
It would be great to see the details of the proof you reference in the video
I put it in my book about Complex Analysis :)
00:00 Intro
0:57 Why power series are important? Example of exp(z)
2:05 General definition for C
4:03 Example. Geometric series + conditions for convergence
9:06 Cauchy-Hadamard theorem
Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.
i need the proof of that elegant fact
As always, great videos. Could you give us a link here to the proof of the nice result (8:48) as a pdf. Thank you in advance!
Good idea. I have my real analysis book where you find a very similar result. But I can also prepare a video or pdf here. It will take some time.
@@brightsideofmaths A pdf would be enough I think! That would be already great.
The proof is now written down in the book about this course. The book is not finished yet, but supporters can already download the preview.
Good videos. Really understood the concept
Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.
thanks very much, teacher. Its really help me a lot :)
You are really welcome. Please also check the pdf version of this video :)
Another nice job 👍
Great video! Thank you!
I would very much like to see the proof.
Hey! Fantastic video, really well-made and comprehensive, and easy to understand as well. I have one request tho, if possible please include proofs of the theorems you mention (such as Cauchy Hadamard, or that power series converge in a ball), or at least provide some links for the same. Much appreciated, thanks!
Thank you very much. Most stuff about power series is proved in my real analysis course: tbsom.de/s/ra
I am also writing a book for this course, which supporters can already download. There, I fill in all the details.
Power Series...?! Haaaa ! "Séries entières" !
Thanks for the video!
HEY NICE JOB . I AM YOUR GREAT ADMIRER.
PLEASE MAKE VIDEOS FOR GEOMETRY FROM (EUCLID TO COORDINATE TO MODERN ONE)
I have a friend that is studying abroad in Germany and when he showed me the Cauchy-Hadamard limit I was kinda confused because we use the d'Alembert rule and it seems to be a lot simpler. Any reason why to use C-H over it?
The root criterion is more general than the quotient criterion, which you mean I suppose?
@@brightsideofmaths
Yeah I meant lim |an+1/an| = 1/R
Can you please give me an example of how this criterion is limited? 😊
You cannot apply it immediately if some sequence members are zero, can you?
Does anyone know how he makes these presentation?
I know it!
@@brightsideofmaths willing to share? XD
@@masteroogway7624 Sure. I use Xournal :)
@@brightsideofmaths thank you very much!
I am an aspiring teacher and your videos have helped me organise so much.
If you have time and are intested, I would love to see your work process for these videos, they are incredible!
@@brightsideofmaths Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.
Energy is duality, duality is energy
Everything in physics is made from energy including mathematics!
Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.
Plz make the prove
It's in my book, which you can download for free as a supporter.
Hello
May i have your email ? I would like to ask you few questions .
Description