Complex Analysis 24 | Winding Number

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This is my video series about Complex Analysis. I hope that it will help everyone who wants to learn about complex derivatives, curve integrals, and the residue theorem. Complex Analysis has a lof applications in other parts of mathematics and in physics.

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(This explanation fits to lectures for students in their first or second year of study: Mathematics, Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[Vannishn]

Hello to you !!! Thank you for every séries you do, they are excellent 🤩

[Zmrocz]

Thank you very much for the explanation. I am surprised that it is so easy :)

[mariolemelin]

Hello Julian. I am surprised that you did not mention the orientation of the curve. Because it is clear that k can be negative. Unless we are supposed to know it from the fact that k is part of Z, which included the negative part. Or am I saying a stupidity?

[anowarali]

If I get subcription/membership then which pdf will I get? The pdf you teaching in YouTube?

[drewtmacha]

For some reason I thought you were very old until today.

[gauravnainwal]

Can you make a series on Abstract Linear algebra, please?

[phy]

That was a briliant video! Do you have any materials about other topological invariants, like e.g. Chern Numbers? I am intrested in applications of topology in physics and it would be great to find some videos about that topic :)

[Muavia-ybgy]

Wonder Full Experience Sir. Thank you so much. I love the way you explain things by visualizing things. Thank you so much again.... 😍
And last thing sir Can you please tell me the software that you are using for Recording lectures and writing. 🙂

[Xaver_]

how come the result of the last integral was exactly the natural log of every z in the path gamma but evaluated at a point t=a ?

[Hmmmmmm]

Doesn’t this proof not work because you need to define arg(z) uniquely? This is form alhorfs book

[anthigeorgiou]

what if the curve passes through the negative real numbers but doesnt go arount the given point shouldnt the integral give a number other than 0?

[karlmudsam]

Yo also can I send some art for that wall, it’s kinda bare yo

[skazzyeahh]

I'm not mean spirited but you look like the gereric version of papa from flammable maths