Complex Analysis 09: Cauchy's Integral Formula

[@Karim-yt4cf]

I have an exam in 2 hours and you just saved my ass. God bless your mathematical bald head sir

[@SigmaSixSoftware]

I’ve been trying to understand this for 2 hours, in a 9 minute video you made it all make sense. Thank you sir

[@IFlyByPlane]

You know someone is a great teacher when they can make complicated problems seem simple. Thank you kind sir!

[@ruddgulit3535]

Sir your one of the best maths teachers I have ever seen

[@regnaldlyamuya1724]

I never thought it would be this much easier God bless you bald man😁👍

[@romarssieverything9667]

Exam tomrrow and after watching son many 20-30 minutes video finally this one made me understand the way we are supposed to do it. Thank you sir!

[@MsPinamalakas]

I don't know how to thank you. you save me. not from exam but from the time I will need to consume to get the knowledge. you enlighten me.

[@runerthereaper3320]

You, good sir, are a savior, thank you very much!

[@situxiaotong7407]

You are a lifesaver.God bless you.

[@mishudhar3746]

Sir, thanks a lot for your lectures. It helps enormously.

[@KnightGab]

Thank you for the clear video on the topic with such simple to understand examples!

[@charleswho5432]

thank you so much! I learn accounting in university but I love mathematics so much. This video gives me a lot of help!

[@gennezvybz]

a math Guru indeed. Thanks so much.

[@kenso5629]

This short lesson was of great help! Thank you

[@Tbone39]

Great video. I have my Adv Calculus exam tomorrow, hopefully I nail it.

[@jjrocksguitar9901]

did you nail it?

[@mcleanephatha]

How can you just look at a function and tell its analytic without doing the Cauchy-Riemann equations? Someone, please help! I often don't know how to go about solving an equation because I can't tell whether it's analytic at a point or everywhere by just looking at it!

[@sebastianerquiaga8494]

Excellent video, clear and concise! Thank you for the help!

[@sasht29]

Such a great teacher 👍

[@tahielgomez]

excellent video!! thanks from argentina

[@ziluzhou4462]

Thank you so much!! What an amazing explanation.

[@jacobchanda4405]

Thankyou so much sir.Your explanation really makes a difference

[@penielnqoboncube7521]

thanks a lot glad i watched this before my exam

[@quantum_encrypt]

Thanks for the vid. What would you do if there was more than one singularity in the region?

[@MathsStatsUNSW]

+hamada fadil mahdi You could use homotopy to rearrange the contours to separate the singularities, but it would be simpler to use the residue theorem (see my later video). The CIF only works for exactly one singularity that must also be of the shape (z-z0)^(-n) for positive integer n.

[@kaash3]

Use partial fraction

[@and_rotate69]

you always answer my doubts

[@rycitomorell5945]

thanks very much for this video!

[@fran_uche]

Thank you very sir. This video helped a lot.

[@smexy2134]

Wonderful video. Thank you!

[@95lflb]

Good on ya John! Great video

[@yassinghareeb5761]

i could never thank you enough!!!

[@ninosawbrzostowiecki1892]

Great video! One question, is the boundary of the contour considered part of the inside of the contour?

[@shuangshuangliu7071]

Thank you so much, now I'm less stressful for my exam

[@sarikasoni9395]

I really need this examples...thnk u soo mch

[@destineos8038]

Thanks you, you save me just before my exam 😅

[@abduaziz79]

Thanks from Saudi Arabia (;

[@ardailgezdi393]

Awesome abstract

[@nikhiljoshy3945]

Your explanation is very good

[@brunolorenzo4574]

Sir why did you differentiate example 4?

[@mariamarques3677]

This is a very good lesson indeed. thank you

[@عبدوفيزيك]

Thanks

[@ammar84ful]

hello prof for the last example, why did u take derivative of e^iz? shoudnt it be just 2pii * f^(1)(-i) ?

[@PaperQuestion]

the integrand is e^(iz)/(z+i)^2, following the formula [lineintegral f(z)/(z-z0)^n+1)=2pi*i f^(n) (z0)/n!] f(z) is e^(iz), which is entire, and the *denominator (z+i)^2 is degree 2, making n=1* all previous examples had a denominator degree 1, making n=0 the notation f^(n) (z0) means taking the nth derivative of the function f(z) in the case of f^(0) (z), f^(0) (z) is the base function, thus why we didn't take the derivative *in the case of f^(1) (z) however, f^(1) (z) is f'(z) as it is more commonly written, meaning to take the 1st derivative* like wise for the following n=2, f^(2) (z) means to take the 2nd derivative of the function hope this wasn't too wordy :D

[@nurulislam5569]

@@PaperQuestion thank you for ur explanation. it helps a lot.

[@JuGGerJuGGs]

You're amazing.

[@fibonacci112358s]

You can tell by the way he holds the pen that he's more used to writing on blackboards. Typical mathematician! ;)

[@michaelroditis1952]

He also tries to let us see what he writes as he is writing

[@hannananan9427]

Thank you so much!

[@maamamphoka6850]

Perfect Thank you sir so much 🙏..

[@nas.nazmul]

very useful. Thanks.

[@shingen911]

Very helpful. Thanks :)

[@mantavyaagarwal7345]

thanx a lot for such a lovely video

[@UsamaAhmedZeki]

So, What i dont understand is when to use the formula and when to use the residue integral theorem

[@vickykong5868]

What if I got a form of ( z node - z ) as the denominator ?

[@arifhakiminadnan4880]

thanks botak ! i could understand it easily .

[@janaranjania2537]

Which country?

[@vigneshs4657]

how to get to work with you in maths

[@shamendraegodawela5555]

UMMAH!!! ADAREI THATTAYO OYAAATA

[@palosantos2495]

Great. Thanks.

[@_blueshift_3976]

4:48 I belive *[ sin (2pi / 3) = negative root 3 / 2 ]* , so that answer there should have a negative

[@khairaldeen3717]

Thank you!

[@nhfstend7649]

thank you soooo much

[@tanveeruddin9032]

i love it.

[@atakancelenk173]

🇹🇷 ÇOK İYİ ANLATIM

[@sebollinweon]

this works only for circles?

[@lordlemmy5108]

nope, any closed shape

[@shivamjalotra7919]

Thankyou

[@abhishekkumar-fl3wz]

thank u sir

[@selvams7061]

practical use of theorem

[@dufashwanayoemmanuel1829]

Try to reduce how you jump the steps in order to convenience the students

[@fordiffa7012]

U best

[@filipuskamati3965]

Thanks For the video..........@hamada fadil mahdi, you partialise

[@safeegull22]

I am not understand this shortcut method

[@ldohlj1]

tnx

[@doaanasr7109]

greaaaat

[@phanie_adela9730]

The camera is a little blunt

[@lemyul]

I fucking hate taking 6 math classes at the same time

[@AlexDunaykin]

dz forgotten in the lefhandside of formula!

[@TheTargetLP]

Needs to be nerfed

[@iamjb007]

u went too fast lol

[@ryushev2000]

KZbin has the option to set playback speed to 0.5x for people like you

[@garyberry3190]

kasian mukanya

[@hlwlife]

thanks