How to Integrate Multivalued Functions | Complex Analysis #20

How to Integrate Multivalued Functions in Complex Analysis. This is something you will need to know when you try to integrate improper real integrals by using complex analysis, which is a standard problem in most courses.

The video will include concepts as:
► Multivalued Function
► Branch Cuts
► Contour Integration
► Improper Real Integrals
► Cauchy's Residue Theorem

LINK TO COMPLEX ANALYSIS PLAYLIST

LINK TO CANVAS

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Consider subscribing, liking, or leaving a comment, if you enjoyed the video or if it helped you understand the subject. It really helps me a lot.

TIMESTAMPS
00:00 - 00:20 Intro
00:20 - 01:20 Theory: Multivalued Functions
01:20 - 04:15 Theory: How to determine the integral of 1/(sqrt(x)(x+2))
04:15 - 12:53 Example: Determine the integral 1/(sqrt(x)(x+2))
12:53 - 13:35 Summary of the main points
13:35 - 13:54 Outro

SOCIAL

HASHTAGS
#TheMathCoach #ComplexAnalysis

[TheMathCoach]

This video is dedicated to a viewer with the name "K" and I hope it can help him/her understand this sort of integrals better. I would love to know what you guys think about the thumbnail? Is it good, any feedback that I can use to make them more "clickable" is appreciated, or just let me know what you would like to see in the thumbnail :)

Have a great night!

[MrOrangeHam]

Very happy to see that you are continuing this series. The best complex analysis tutorials on YT!!!

[PunmasterSTP]

I saw that notification and I knew it was gonna be good. I can't thank you enough for putting out such a high-quality educational resource into the vast expanse that is YouTube. There's a few channels that I feel have a sense of community, and yours is definitely one of them. Keep up the amazing work, and I'll pop in every now and then to try to learn a thing or two!

[aoleon]

You explanation is visually satisfying.

[nuriarodriguez]

So glad I found your channel. You explained the concept very well. Thank you!

[punditgi]

Excellent explanation! Thanks for the videos!

[diogoprudente]

I really like your videos. You have a great way to organize your vids

[bkxvilh]

As expected, best explanation ever, thanks! Is it possible do an example with an improper integral using Jordan's lemma (Fourier, cosine, sine integral)?

[alihanemretunc]

Hello. These videos are really well explained and visualized, thank you. I don't quite understand how to choose a contour for this type of integrals though. How can I choose the right contour, any tips maybe?

[matsushitahisashi]

Where can I find your definition about branch cut? lecture #19?

[euler]

hello "why haven't you uploaded videos for long time?" I really love your videos about complex analysis. "will this video be the last one in your complex analysis playlist? " or will you upload more videos about complex analysis like the relationship between zeta and gamma function in complex analysis, zeta functional equation and summing series by using residue theorem, etc .

[maomi]

Why z+2 turned to 2-r in the denumerator

[maomi]

Please Crack the Fourier analysis also and PDEs

[youngzuczek]

How did the z+2 transform to R-2 at 6:55