Complex Analysis 17 | Complex Integration on Real Intervals

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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)

[kingshukdutta]

I have a complex analysis exam day after tomorrow. Your videos have been really helpful! Can you make a video on residues in the future?

[nocomment]

U r great 👍 mathematics is incomplete without u

[maohejiang]

the walking god series, saving my life in math courses

[KM-omhm]

In this video you have changed the complex function |Z-Z0|-1=0 (explicitly)[a circle without radius of 1unit, Z0 is just 0+i*0] into e^it (parametric form)


Can we directly integrate f(z)dz ?

[guohaoyang]

May I ask when proving the absolute value inequality, why the integral of C^(-1)γ(t) doesn’t have imaginary part?

[qianliu]

For the proof, whether c^-1 * c should equal to 1?

[mariolemelin]

About the example exp(i*t). The final result I get is 4*i (I did 2 times the integral from 0 to Pi - if you don't do that, you get 0). Am I right? And as usual, very interresting video.

[hexeldev]

why is c^-1 times gamma only real? 8:50

[KM-omhm]

I wonder how could they think something like this