I had an introduction to complex analysis last semester during my electrical engineering undergrad. Churchill and Zill were my best friends, hahaha. I actually found your channel while searching for complex analysis content. Keep it up with your content, it's very helpful and inspiring.
Im also going to be starting a major in EE this fall so I was just curious, was your intro to complex analysis part of an EE course, or did you take a math dept course in complex analysis?
It’s been a while since I was a student (undergrad in 2020), but have you used the Alfhors complex analysis? Alfhors has to be the weirdest textbook I’ve read. It’s in a completely narrative style (not in a statement-proof format) and it goes through some pretty advanced concepts not typically found in an undergrad semester-long complex analysis course. There were sections in Jacobi theta functions, doubly periodic functions, Riemann mapping theorem, Schwarz Christoffel formula, analytic continuations (Monodromy Theorem), etc. It wasn’t a part of the book, but we discussed voronin universality when we were going through the zeta function section 😂 It was one of the wildest classes I’ve ever done assignments in (algebraic geometry takes the cake there) but I took a lot out of it even though I don’t use a lot of this math anymore. Love watching your videos because it always reminds me of my student days. Good luck on your exams! Love your content.
I actually learnt complex analysis off Stein and Shakarchi. Couldn't get used to its writing style during the semester, but came back and appreciated its elegance at a later date. In fact S&S used these definitions: Holomorphic = complex differentiable; Analytic = can be expressed as a convergent power series. And one can prove that a function is holomorphic in an open set if and only if it is analytic in the same open set. This explains why the two terms are freely interchangeable. As for the definitions of interior and closure of A, actually "largest open set contained in A" and "smallest closed set containing A" are actually effectively the definitions used in any dedicated topology class/book. They write "union of all open sets in A" and "intersection of all closed sets containing A" because this is the exact representation of the sets - you find the largest open set contained in A by taking the union of all open subsets of A etc. So they actually mean exactly the same thing. But I do agree it is much easier to think in terms of largest open set and smallest closed set.
Also, yes, we want to hear you drone on and on about Complex analysis. You're a fascinating human with a complex field of study that entices the rest of us - please keep sharing.
You are 100% amazing! I'm studying for my state exams and depend on putting everything in one notebook to study with. Having too much information scattered about is very confusing and you can miss things. Don't you love complex exams--it keeps one regular just thinking about it LOL. With all that high anxiety...just do it and try. I mean we are all going to die in the end so why not try.
Let f:U→ℂ be continuously differentiable in U an open subset of ℂ then f is holomorphic if 𝜕f/𝜕z̄=0 at every point of U. Ex: The function f(z)=1/z is Meromorphic, it's not holomorphic at z=0, but at any other point in ℂ it complies with the definition, so it's holomorphic for all z ∈ ℂ-{0} and 0 is a singularity point.
Writing a textbook form notes based on a textbook reminds me of 30 rock when Jenna gets the fake award for "Best Movie Based on a Musical Based on a Movie" for the mystics pizza musical movie haha. Also tbh it's how most textbooks get written, just with a few years of refinement based on using the notes to teach courses and usually updating them based on experience from your research and teaching; and changes in student expectations etc.
cool stuff! Thanks for sharing. 10:03. Totally agree with that. I intend to self study real and complex analysis soon. Best of luck on your exam! - fellow grad student
I’m glad I’m not the only ambitious person that has attempted to write their own book on a math subject, I did workbooks on trigonometry and intermediate algebra
the way i learnt it, analytic functions are locally equal to a convergent power series everywhere in a domain and holomorphic functions are complex differentiable everywhere in a domain. the difference is that the domain of analytic functions can be something other than complex numbers (eg bounded operators). if the domain is the complex plane or open subsets, holomorphic and analytical functions are exactly the same ( en.wikipedia.org/wiki/Analyticity_of_holomorphic_functions ).
If a function is analytic, its real and imaginary parts satisfy Laplace's equation in plane polar coordinates. If a function satisfies Laplace's equation, it can be the potential of a conservative field. That has great applications in Physics, in areas such as Electrodynamics, Mechanics, Fluid Dynamics and many others.
It feels like math is limitless we still discover to this day new theorems new conjectures and new definitions But the thing is that if you want to study mathematics especially advanced math you have to specialize in one or two areas but not more like you can't just have a good grasp of knowledge in every branch in mathematics because that is impossible one perhaps would prefer topology over modern algebra and one could specialize in number theory or analysis ...etc
your videos are my equivalent of subway surfers gameplay while i study
This is just so smart. I wish I did this when I was in college
I had an introduction to complex analysis last semester during my electrical engineering undergrad. Churchill and Zill were my best friends, hahaha. I actually found your channel while searching for complex analysis content. Keep it up with your content, it's very helpful and inspiring.
Im also going to be starting a major in EE this fall so I was just curious, was your intro to complex analysis part of an EE course, or did you take a math dept course in complex analysis?
@@brandonbennett4970 It's part of the course, a very important one. Good luck with your course!
@@LucivaldoJunior ah okay, thanks!
Gosto muito do seu canal. 👍
It’s been a while since I was a student (undergrad in 2020), but have you used the Alfhors complex analysis? Alfhors has to be the weirdest textbook I’ve read. It’s in a completely narrative style (not in a statement-proof format) and it goes through some pretty advanced concepts not typically found in an undergrad semester-long complex analysis course. There were sections in Jacobi theta functions, doubly periodic functions, Riemann mapping theorem, Schwarz Christoffel formula, analytic continuations (Monodromy Theorem), etc. It wasn’t a part of the book, but we discussed voronin universality when we were going through the zeta function section 😂 It was one of the wildest classes I’ve ever done assignments in (algebraic geometry takes the cake there) but I took a lot out of it even though I don’t use a lot of this math anymore.
Love watching your videos because it always reminds me of my student days. Good luck on your exams! Love your content.
I actually learnt complex analysis off Stein and Shakarchi. Couldn't get used to its writing style during the semester, but came back and appreciated its elegance at a later date. In fact S&S used these definitions:
Holomorphic = complex differentiable;
Analytic = can be expressed as a convergent power series.
And one can prove that a function is holomorphic in an open set if and only if it is analytic in the same open set. This explains why the two terms are freely interchangeable.
As for the definitions of interior and closure of A, actually "largest open set contained in A" and "smallest closed set containing A" are actually effectively the definitions used in any dedicated topology class/book. They write "union of all open sets in A" and "intersection of all closed sets containing A" because this is the exact representation of the sets - you find the largest open set contained in A by taking the union of all open subsets of A etc. So they actually mean exactly the same thing. But I do agree it is much easier to think in terms of largest open set and smallest closed set.
Holy... this is genius.
I have to do this now while I'm still in my studies. This companion textbook is ingenious! 🎉
Also, yes, we want to hear you drone on and on about Complex analysis. You're a fascinating human with a complex field of study that entices the rest of us - please keep sharing.
Ever since I saw the Real Analysis video I couldn't wait for the Complex Analysis video! Good luck on writing this :3
You are 100% amazing! I'm studying for my state exams and depend on putting everything in one notebook to study with. Having too much information scattered about is very confusing and you can miss things. Don't you love complex exams--it keeps one regular just thinking about it LOL. With all that high anxiety...just do it and try. I mean we are all going to die in the end so why not try.
Let f:U→ℂ be continuously differentiable in U an open subset of ℂ then f is holomorphic if 𝜕f/𝜕z̄=0 at every point of U.
Ex: The function f(z)=1/z is Meromorphic, it's not holomorphic at z=0, but at any other point in ℂ it complies with the definition, so it's holomorphic for all z ∈ ℂ-{0} and 0 is a singularity point.
Writing a textbook form notes based on a textbook reminds me of 30 rock when Jenna gets the fake award for "Best Movie Based on a Musical Based on a Movie" for the mystics pizza musical movie haha. Also tbh it's how most textbooks get written, just with a few years of refinement based on using the notes to teach courses and usually updating them based on experience from your research and teaching; and changes in student expectations etc.
Amazing!
I'll buy it. Just never give up finishing it
cool stuff! Thanks for sharing. 10:03. Totally agree with that. I intend to self study real and complex analysis soon. Best of luck on your exam! - fellow grad student
I’m glad I’m not the only ambitious person that has attempted to write their own book on a math subject, I did workbooks on trigonometry and intermediate algebra
the way i learnt it, analytic functions are locally equal to a convergent power series everywhere in a domain and holomorphic functions are complex differentiable everywhere in a domain.
the difference is that the domain of analytic functions can be something other than complex numbers (eg bounded operators). if the domain is the complex plane or open subsets, holomorphic and analytical functions are exactly the same ( en.wikipedia.org/wiki/Analyticity_of_holomorphic_functions ).
god i wish i had this for my planetary science degree
Im trying to learn real analysis and get used to work with epsilons and deltas... Im freaking out
You often mentioned "commit to memory". What process do you go through to commit a 2 or 3 page proof or concept to memory?
I used the word holomorphic all the time. I never heard it could be called analytic for this.
Thanks for the vid brah
which pen do you use for writing such things?
Lars Ahlfors has entered the chat
Aight imma head out
When will this be released
do analysis grad students study several complex variables?
Is there a chance we could have a copy of your draft of your Analysis books?
Is there is any way to access your complex analysis notes?
Can you posted it online like in pdf format?
Bro , other then power series expansion at a point in complex plane , what is the other use of an Analytic Function ?
If a function is analytic, its real and imaginary parts satisfy Laplace's equation in plane polar coordinates. If a function satisfies Laplace's equation, it can be the potential of a conservative field. That has great applications in Physics, in areas such as Electrodynamics, Mechanics, Fluid Dynamics and many others.
what is your video recording setup?
Can you suggest me the best book for self learning real analysis as I am beginner in it
hopefully we get to see your face one of the good days
Will someone tell me, how far mathematics can be discovered or it can be studied for centuries
It feels like math is limitless we still discover to this day new theorems new conjectures and new definitions
But the thing is that if you want to study mathematics especially advanced math you have to specialize in one or two areas but not more like you can't just have a good grasp of knowledge in every branch in mathematics because that is impossible one perhaps would prefer topology over modern algebra and one could specialize in number theory or analysis ...etc
@@HIVEEX01 Oh okay that's good, Thanks 😊
@@abhisheksoni9774 no problem have fun learning math 😄
@@HIVEEX01 Yeah sure, you too 😊
yoo
Subs get a discount right?😢😂😂
This is horrifying
Why?
@@amadeusamadeus7896 I'm too stupid to understand complex analysis.
Prove the riemann hypothesis then
Pass