Cauchy Integral Formula with Examples - Complex Analysis by a Physicist 

"being a physicist I bound to do something to upset the mathematician" got me 😂😂 Thank you for this, I've been struggling to understand my lecturer for complex analysis and your video helps me tremendously!

Complex analysis exam later today and this video might just have saved my life ty Nick!

This dude has 2.64k subs?How? He is that good. Straight to the point but understandable. Bravo Nick!

I tried many videos in few youtube channels to understand this. But you are the best💜️

Beautifully explained, Thank you.

Good work, I felt complex analysis was not as complex! Thanks!

Well explained Nick! 🔥

This is bound to make the mathematician happy!

This is so helpful. Thank you man!

very very helpful! thank you so much

Well Expained Thanks

A really big thank you, I understood it because of your exemple, something my professor doesn't do!!!

Thanks man this is really helpful

Thank you !

Great content bruv

Complex analysis was one of my favourite courses at the university of the west indies, cave hill campus. I have a few more ' what if' questions, not only in the field of Complex analysis, but in other areas also 2:10

Besides these really weird pis which neither do look like lowercase pis nor like capital ones, its a very good video. Cheers!

Thank you sir 😌

Very good video, thank you very much!!!

Thanks Nick

Thank you brother

Wonderful

This was a great video . The only thing I thought could be better were the examples number and complexity could've increased .

Thank you sir!

Thank you so much dude

Can n be generalized to all real number? I face fractions all the times.... (E.g. n = 5/2)

What happens if the simple closed curve is not positively oriented? 2:10

Dankeee

👌👌

Why is it n!/2*pi*i in the formula, but when doing the solution you say 2*pi*i/n! ?

i don`t understanded please show more example

Nice video!! one question tho, at 8:12 why does f(z0) = the derivative of f(z)?

EDIT: This was indeed a stupid question on my part!! I forgot a basic fact about fractions 🤣. No need to answer this question, but I'll leave this comment up here, just in case someone has a mental relapse I did! If you want a good laugh, feel free to read my unedited question below 🤤 This may sound like a stupid question, but can f(z) be a polynomial? My reason for asking is this: Suppose we are integrating over a closed contour that does NOT include the point z=0 but does include a complex z_0 (where z_0 is not zero). The solution to this integral, assuming the integrand has the form f(z)/(z-z_0), is 2πif(z_0). But now, what happens if I rewrite the integrand as (f(z) + z_0)/(z - z_0 + z_0). All I've done was shift both the numerator and the denominator by z_0. z_0 is just a complex number, and not the integration variable, so I think this shift should be allowed. If I define a new function, say g(z) = f(z) + z_0, then the integrand is now g(z)/z. Remember that we have a contour that does not surround z=0. Therefore, the integral should equal 0, but according to the integral we started with, it should equal 2πi*f(z_0). This solution does not agree with the true solution provided by this integration rule (or identity or whatever it's technically called...😅). What am I misunderstanding about the limitations of solving an integral like this?

To overcome the problem. But i will leave you to work that out 9:27

Please 🙏 show solved examples

Hey man, can we speak on private somehow ? i really need help understanding somthing.

Why (2pi.i)/1

The way the cauchy formula is stated by you, suggests to the learner that you are trying to evaluate f(z) nought. However you rearranged the formula so that you could evaluate f(z). This is a common mistake of teachers and lecturers. There is a way to overcome overcome

Stop Back music

I find the examples too simple , somewhat more complicated ones would show more of this very useful formula

who the hell is coshy?