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Thank you for another excellent video. I love complex analysis, and have always found your complex analysis videos to be the best.

👍

Shouldn’t x = 0, 1?

Your Chi's look more like X's. Yuck.

i thought it was a finite expansion lol. i was also thinking of pi as an exponent, i guess it'll have inifinite terms like these.

Hi, Can you explain the error function `log(n)/10` please.

goddamn math is so fucking boring it should basically be done by machines at this point, why do we humans even bother at this point it's just a series of subtle and pedantic rules applied over and over again? we should do it all via computers except for maybe 1000 humans who dedicate their lives to actually advancing the field. just kill me already.

What if you get a case where you cannot easily find a square number for the square root? Eg: x^2+5x+1 = 0 (mod 13)

First!

why not 2x^2+16x+34=t^2

Hey, I'm not sure what the purpose of the video is. I teach math at university, and I gotta tell you that substituting 2x^2+16x+34 gives you an immediate answer to the problem. No logarithm no sec function. Did you just wanna try to make things extra complicated? Seems a little disingenuous and leads people to believe that math is difficult. This video does math a disservice.

If you divide that final equation by 2 on both sides, don't you get a different radius?

Great job as always. Thank you!

To nie jest szereg, dziecko, a jego kawalek, czyli wielomian Taylora ) Dislajk.

Thank you! Especially for explaining this with an actual example. I've been going nuts trying to figure out residues and everything I look in always seems to hide the ball.

Very useful, but I don't think I quite get why (A = -5/4) instead of (A = 4/-5).

These are great! But I have a question/problem arising from 8:05 in video. If we expect pointwise convergeance then result holds and is good and wholeseome. If I say, well look - I need an error bound on this. If it approaches a fixed point with error bound plus or minus one ± 1 say inclusive on [-1, 1] then a finite number of ambiguities arise. Can I say it does converge to zero with error ε in [-1, 1] or equivalently it converges to 1 within error ranging [-1, 1] or converges to -1 within error ranging [-1, 1] AS far as I am concerned, say, an error bound of ±2 on the limit value is perfectly acceptable 0 ±1 or 1±2 or -1±2 is acceptable on ± infinity ?

Amazing 🤩

Not clear video

Thank you so much

2025 who'se watchign

hell yeah man, thanks for the help

I echo the previous three comments and ponder: Hey! Where is Prime Number Theorem? I can't find it - googled it and results speaks in a language I have yet to understand. I am sure your version will make more sense to me (please?)

This is going to make me kill mysefl

In 15:37 -3 is congurent to 5 mod 8 and not 5 mod 4 right?

Thank you! So helpful!

Of cosh you went on a tangent, and it was complex, but it was also great!

Thanks Chief

good lecture to draw graph. It tolds me the fundemental therems for graphing. Thanks from South Korea.

domotro led me here. good video..

Very helpful and clear presentation. Thank you!

Math magic!

Technically, pi/2 is the Cauchy principal value, right?

Du bist großer wunderbar!

Great video! Thank you.

Excellent video. I love complex analysis.

Great video! Thank!

Thank you for this video. At (0:53), you say the sum of prime numbers is odd. Did you mean to say the number of primes, or the sum of primes?

You are brilliant!

Sir, I have a confusion in these questions, like why you didn't write cosec(πz) as 1/ sin(πz) and then find the residue at z=n ( where n=+-1, +-2,,,,). Please help me in it

That was great. Thank you ; )

The poles of 1/1-e^z are given by 1-e^z=0 Please explain this sum

Thanks! This is a great video

Love what you are doing but ... @ 5:25 and earlier x = 0 ⟾ dy/dx = -1 (not y) and d²y/dx² = -6 (not y) And of course as you know at x = 0 y = 4 That said I think what you are doing is great!

Find the last three digits of the number 19^97

Deep in cal 2 and never understood U substitution until now. Something clicked here. Thanks!

Thank you so very much Professor

Thanks so much!!

Great explanation, thank you sir, from next time sir, increase the sound of your voice it'll be really helpful, thank you