Complex Analysis 35 | Application of the Residue Theorem

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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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#Analysis
#Calculus
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#curveintegral
#integration

(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)

[riadsouissi]

I know that was not the point of the video, but leaving sin(pi/6) like that and not replacing it with 1/2 left me hanging with a feeling of emptiness...

[danielblanco]

Mr. I cannot thank you enough, your video series for Measure Theory and Complex Analysis saved me from failing my Analysis III exam. Keep up the good work!!

[smoosq]

thank you, really detailed explained, helped me a lot.

[mortimertz]

such a good play list. please consider Lie groups, Lie algebra, Haar measure.

[StratosFair]

Thank you for this series, I learned a lot !! It would be great if you could consider extending it by covering some more advanced topics (residue at infinity, conformal maps, Rouché's theorem...) :)

[wonjonghyeon]

Why did not you compute the value of sin(π/6) at the end?

[kehoerg]

Perhaps not the right place to ask this question you might think, but as the people who are watching this are so up to date with your work, they're likely to be someone in the same shoes as myself....

Having finished a degree 10 years ago, and not being proud of my result, I am attempting to learn things again.

Without exams to sit, there is seemingly no pressure to get it done, and if I'm honest I am failing. I can't but help think things like, why am I even doing this? What am I trying to prove.

Has anyone any advice, maybe even the content creator himself. Thanks in advance.... am I alone in this I wonder?

[alicebobson]

best video on this ever, way better than my lectures!

[funnyvideo]

Why we take only upper half of the circle?

[ohjoshrules]

Thank you for your videos. They have been so so so helpful in my undergraduate studies

[kamalsaleh]

But how do we calculate the roots so quickly? Any videos you recommend? Also, I really love your videos!

[Independent_Man]

5:44 you are a mathematician so I wanted to ask you if it's correct practice to write the inequality as <= O(1/R) ? Certainly, writing it as = O(1/R) is correct so "<=" in "<= O(1/R)" is redundant but is it acceptable notation? I write research papers in engineering so we get away with imprecise notation but mathematicians are more rigorous about this stuff.

[numb]

Hi, I have a problem understanding Rouche's theorem, but I couldn't find any videos on it in your videos. I was wondering if you have covered that topic. Thank you!

[lauraponti]

very nice videos! Thanks for the explainations! I just do not understand, how you find so quick the residues for z1, z2 and z3.

[darcash]

Complex analysis seems awesome but what does real analysis do?

[GeoffryGifari]

on the last part when we discard the cos( ), do we implicitly take Re( ) of the entire contour integral? so that the real part of a contour integral must equal the integral we want?

[karinablanchard]

Where can I find more info on standard estimates? I am lost on that part

[marytheraspberry]

Hello. Your videos are very useful. I thank you for all the efforts you put in them.
I have a request: can you make a video series on Fourrier and Laplace transforms? Thank you.

[johnlazarus]

Thanks for your videos! I have an issue with the formula for simple poles (h(z) /g(z) ) used. When can we use it? I tried solving with the formula lim z-z0 [(z-z0) f(z)] to calculate the limit and the answers are different. Also tried it for the improper integral for f(x) = x^2/(1+x^4) and had a different answer also.

[MrChickenjoe]

05:03 Why is there no Pi in the power? Since its a halfcircle the power should be i*pi*t right?
I think it does not affect the estimation however.