The shortest path to a solution of a real problem is through the complex domain. It has been some 20 years since I have had complex analysis and you have reminded me of its beauty through your lectures. I remember that in our class we have proved the fundamental theorem of algebra using complex analysis (every n-th order polynomial equation has exactly n roots), perhaps you could add something like this just to show the power of working in complex domain.
I just watched it through. This needs to be spread for all of humankind. Although the ML derivation was not clear to me here. But everything else is legendary status.
@@EigensteveYour channel is a goldmine! This morning I found more stuff that I’ll watch later. BTW, I’m wondering if you have any hints for me to deal with homotopic problems, based on the complex analysis videos you have made.
@@juniorcyans2988 That is great! Good question... I don't have any lectures on this, but some of the old engineering applied math textbooks might have material... maybe Courant and Hilbert or Simon and Reed... not sure, but I found these used for not too much.
Great videos....🙂 At first I thought it would be difficult but you made the complex analysis easy to understand. I watched all the videos in the playlist ...😀
Great lecture as I prefer worked examples to purely algebraic proofs. Why are a3 and a4 included in the calculation as they lie outside C? Are the always connected by narrow pathways (which cancel)?
It is interesting that if he includes conformal mapping this will be a primer for different S-Matrix based ideas for current topics in high high energy physics.
The shortest path to a solution of a real problem is through the complex domain. It has been some 20 years since I have had complex analysis and you have reminded me of its beauty through your lectures. I remember that in our class we have proved the fundamental theorem of algebra using complex analysis (every n-th order polynomial equation has exactly n roots), perhaps you could add something like this just to show the power of working in complex domain.
Nice pictures and descriptions, top work here. Thank you. So interesting that the singularities arise in the complex numbers but not on the real plane
I just watched it through. This needs to be spread for all of humankind. Although the ML derivation was not clear to me here. But everything else is legendary status.
Very nice to see such a superb digitally demonstation❤❤
I watched several times during this semester and I feel I understood better this time.
Glad to hear it :)
@@EigensteveYour channel is a goldmine! This morning I found more stuff that I’ll watch later. BTW, I’m wondering if you have any hints for me to deal with homotopic problems, based on the complex analysis videos you have made.
@@juniorcyans2988 That is great! Good question... I don't have any lectures on this, but some of the old engineering applied math textbooks might have material... maybe Courant and Hilbert or Simon and Reed... not sure, but I found these used for not too much.
I needed quick recap of all the parts of complex integral and this video nicely has it. Thank you!
Glad it was helpful!
Great videos....🙂 At first I thought it would be difficult but you made the complex analysis easy to understand. I watched all the videos in the playlist ...😀
Fantastic Video. Thank you very much :)
Great lecture as I prefer worked examples to purely algebraic proofs.
Why are a3 and a4 included in the calculation as they lie outside C? Are the always connected by narrow pathways (which cancel)?
What are your definitions of continuous deformation?
Great videos you did Steve! I just wanted to know if will be additional videos including conformal mapping?
It is interesting that if he includes conformal mapping this will be a primer for different S-Matrix based ideas for current topics in high high energy physics.
Awesome class!
Glad you think so!
12:43
Is there a 1/2 factor missing here /
Hello! Could you make videos about math modeling for control systems? :)
It’s easier with a quarter circle, then you only have to calculate 1 residue.
Wonderful explanations! Maybe allow yourself a break every once in a while ;)