Magnificent ! I still remember this course I took thirty years ago at university in books like Rudin, Ahlfors and, of course, Henri Cartan...Beautiful memories..
I've been looking for an explanation of the connection between conservative vector fields, analytic functions, and exact differential equations for the longest time now and this video along with some from your vector calculus and PDEs series basically cleared most of it up, thanks a lot!
I really like the basic bring back at the beginning. That we are dealing with complex numbers that are going into functions that are ALSO complex. The increased "dimensionality" really does need to be driven home. It is one of the most intimidating parts.
Unfortunately Goursat is not on the Eiffel tower, but might be only because he was too "young" at that time. All of the people whose name is on the Tower had passed away by the time the Tower was inaugurated, except Hippolyte Fizeau, who died in 1896. Goursat died in 1936.
Another great video. I have not yet watched this whole series, so forgive me if this has been included: I recently watched GoldPlatedGoof ‘Fourier Analysis for the rest of us’. He outlines how epicycles can be used to draw anything you like via Fourier decomposition. This helped me take another step towards understanding Fourier and complex analysis. I’m sure you have seen epicycles drawing Homer Simpson. The fact that, theoretically, one can computationally produce an equation from scribble is powerful and pedagogically tremendously helpful. Would love to see your take on this.
To sum up: Is there any direct relationship between what happens in R and what it means and what happends in C and what it means in both criss-crossed subsets?
Maybe I m late but: Does this path - independence in the complex plane has something to do with the Principle of Minimum Action, which could be prooved using Functional Analysis too?
okay what is your rig? I can hear the distinct satisfying squeak of a marker on a white board and yet this looks like you're writing on some sort of imaginary plane in front of you. are you filming in front of a greenscreen writing on a pane of glass or something?
Hahaha that would be cool, but he's not writing backwards. The technology that he's using to produce this video allows him to write normally and flips everything in post-production.
OMG BEEN STRUGLING TO UNDERSTAND THIS FOR EXAM BUT YOU HAVE MADE EVERYTHING EASIERR.. THANKYOU SIR, SALUTE:)
I know you are busy. Thank you for distilling this down. We are very grateful...please keep going!
Magnificent ! I still remember this course I took thirty years ago at university in books like Rudin, Ahlfors and, of course, Henri Cartan...Beautiful memories..
thank you for these numerous and long videos, they are great supplementary material to the real course!
I've been looking for an explanation of the connection between conservative vector fields, analytic functions, and exact differential equations for the longest time now and this video along with some from your vector calculus and PDEs series basically cleared most of it up, thanks a lot!
I really like the basic bring back at the beginning. That we are dealing with complex numbers that are going into functions that are ALSO complex. The increased "dimensionality" really does need to be driven home. It is one of the most intimidating parts.
Unfortunately Goursat is not on the Eiffel tower, but might be only because he was too "young" at that time. All of the people whose name is on the Tower had passed away by the time the Tower was inaugurated, except Hippolyte Fizeau, who died in 1896. Goursat died in 1936.
This topic really helps to compute the inverse Laplace transform for fractional orders integrators, thank you so much this lectures are excellent
at 24:55 , I think, it should be u = Gy and v = Gx for vdx + udy to be an exact differential.
Another great video.
I have not yet watched this whole series, so forgive me if this has been included: I recently watched GoldPlatedGoof ‘Fourier Analysis for the rest of us’.
He outlines how epicycles can be used to draw anything you like via Fourier decomposition. This helped me take another step towards understanding Fourier and complex analysis.
I’m sure you have seen epicycles drawing Homer Simpson. The fact that, theoretically, one can computationally produce an equation from scribble is powerful and pedagogically tremendously helpful. Would love to see your take on this.
Hey Steve, thank you! Are you planning to make Real Analysis series as well? It would be a great supplement to the Complex Analysis one you have?
Are you left handed or can you write backwards?
yes =)
To sum up: Is there any direct relationship between what happens in R and what it means and what happends in C and what it means in both criss-crossed subsets?
This dope... I'd wished my college lecturer is like this... He is just a bit making mathematics Hard🙄🙄
do you have lessons on modern numerical computation?
@23:31 so cute, melts my heart
Maybe I m late but: Does this path - independence in the complex plane has something to do with the Principle of Minimum Action, which could be prooved using Functional Analysis too?
23:37
Link to the pdf please.
Thank You
is there some inherent connection between complex integral and vector calculus, somehow they look quite similar
I did rather poor on complex analysis back in college, this ought to be really good for me❤
Great, but where is the pdf?
34:14 Super cool!
You made me think about analytic regions as inocent regions and non analytic regions as demons
okay what is your rig? I can hear the distinct satisfying squeak of a marker on a white board and yet this looks like you're writing on some sort of imaginary plane in front of you. are you filming in front of a greenscreen writing on a pane of glass or something?
I cant stop thinking how this is filmed
Those squiky sounds the marker does on the glass are painful
imagine doing this writing backwards, let alone doing this itself LOL
Hahaha that would be cool, but he's not writing backwards. The technology that he's using to produce this video allows him to write normally and flips everything in post-production.
@@justintiger9 oh my god !!! 😂😂😂😂 thanks bro
Why are you spending so much time learning mathematics?
To impress my friend in parties.