Complex Analysis 18 | Complex Contour Integral

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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)

[StratosFair]

I really liked the appendix at the end :)
Question out of curiosity : is it possible to extend the definition of complex integral to non differentiable lines (e.g. the sample path of a Brownian Motion) ?

[keyyyla]

Which program/software do you use to create the images on the thumbnails?:)

[vkoptchev]

Not sure why you try to explain the γ’ in such way. It simply comes from z=γ(t), dz=(dγ/dt)dt

[PrzemyslawSliwinski]

Do I have déjà vu?

PS
13:05 - Now I know how much you like the idea of a cliffhanger! ;)

[temjenlongkumer]

In the definition of contour integral, what if the integral on the Right Hand Side does not exists?
I mean, I couldn't see any reason that guarantees that the integrand on the Right Hand Side is integrable between a and b

[GeoffryGifari]

is it right to say that γ' is there because differential dt is only defined on the real line, and the integral can only be indirectly mapped into [a, b] through γ?

[malawigw]

Yeah this was a nicer version of an already nice video!

[KM-omhm]

I still don't have a very clear idea what does int(f(z)dz) geometrically mean