Here we go over the Cauchy Integral Formula in complex analysis. We also do a few examples that utilize the Cauchy Integral Formula in complex analysis. Music: Mirror Mind - Bobby Richards
Пікірлер: 51
@ruthanderson2518 Жыл бұрын
"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!
@bellzon40862 жыл бұрын
Complex analysis exam later today and this video might just have saved my life ty Nick!
@nspace-cowboy2 жыл бұрын
Glad I could help!
@tinoe25chitah8 ай бұрын
This dude has 2.64k subs?How? He is that good. Straight to the point but understandable. Bravo Nick!
@anuoluwapoomobolaji5642 Жыл бұрын
Beautifully explained, Thank you.
@murtazaabasskhan1103 Жыл бұрын
Good work, I felt complex analysis was not as complex! Thanks!
@martinkimu8736 Жыл бұрын
Well explained Nick! 🔥
@kavindumalshan6802 жыл бұрын
I tried many videos in few youtube channels to understand this. But you are the best💜️
@nspace-cowboy2 жыл бұрын
Thank you so much 😀
@joelasaucedo5 ай бұрын
This is so helpful. Thank you man!
@rudycummings46719 ай бұрын
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
@MichaelMarteens7 ай бұрын
This is bound to make the mathematician happy!
@wilfredtimi8287 Жыл бұрын
very very helpful! thank you so much
@samenterprise1343 Жыл бұрын
Thanks man this is really helpful
@johnnysasquatch30032 жыл бұрын
Besides these really weird pis which neither do look like lowercase pis nor like capital ones, its a very good video. Cheers!
@emileplante59069 ай бұрын
A really big thank you, I understood it because of your exemple, something my professor doesn't do!!!
@nspace-cowboy9 ай бұрын
Happy to help!
@maharnabiiestshibpur6570 Жыл бұрын
Thank you sir 😌
@abhinavm38082 жыл бұрын
Thank you !
@MossesRoss Жыл бұрын
Thanks Nick
@fisicaematematicacomjean Жыл бұрын
Very good video, thank you very much!!!
@nspace-cowboy Жыл бұрын
Glad you liked it!
@azizkash286 Жыл бұрын
Thank you brother
@israelopara4786 Жыл бұрын
Great content bruv
@johnmuchori6605 Жыл бұрын
Wonderful
@rumbidzaiphoto13992 жыл бұрын
Thank you sir!
@nspace-cowboy2 жыл бұрын
You are welcome!
@adityakushagra69382 жыл бұрын
This was a great video . The only thing I thought could be better were the examples number and complexity could've increased .
@adityakushagra69382 жыл бұрын
or there could be a part 2 to this video for that ! your explanation was quick and simple 😊
@7quantumphysics2 жыл бұрын
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?
@jurgenmuller43172 жыл бұрын
Thank you so much dude
@nspace-cowboy2 жыл бұрын
No problem
@abcpsc Жыл бұрын
Can n be generalized to all real number? I face fractions all the times.... (E.g. n = 5/2)
@rudycummings46719 ай бұрын
What happens if the simple closed curve is not positively oriented? 2:10
@nahuu4481 Жыл бұрын
Dankeee
@elgatito002 жыл бұрын
👌👌
@brokkoli51222 жыл бұрын
Nice video!! one question tho, at 8:12 why does f(z0) = the derivative of f(z)?
@asdfmy12342 жыл бұрын
Because f(z)=exp(z) the derivative is itself: f’(z)=exp(z)
@rudycummings46719 ай бұрын
To overcome the problem. But i will leave you to work that out 9:27
@gregoryojei7407 Жыл бұрын
Please 🙏 show solved examples
@eyobkenfeshekedir4802 жыл бұрын
i don`t understanded please show more example
@danielkane66907 ай бұрын
Why is it n!/2*pi*i in the formula, but when doing the solution you say 2*pi*i/n! ?
@bro8221 Жыл бұрын
Hey man, can we speak on private somehow ? i really need help understanding somthing.
@nicholusmwangangi7960 Жыл бұрын
Why (2pi.i)/1
@nspace-cowboy Жыл бұрын
I'm not immediately sure. I'm sure a derivation of the Cauchy integral formula would probably explain why.
@rudycummings46719 ай бұрын
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
@androidtv45292 жыл бұрын
Stop Back music
@renesperb Жыл бұрын
I find the examples too simple , somewhat more complicated ones would show more of this very useful formula
@nspace-cowboy Жыл бұрын
Thanks for the feedback. I'll try to add some more complicated examples in future videos.