Cauchy's Residue Theorem with Examples | Complex Integration | Complex Analysis #16

[@TheMathCoach]

Good morning guys, is the audio levels fine in this video? The same video with the proofs will release next sunday!

[@MrOrangeHam]

Audio levels were fine for me. Nice job with the video.

[@TheMathCoach]

@@MrOrangeHam Great, thanks for the quick feedback! Did not know if I should have taken it down and uploaded with increased audio levels!

[@TheMagicMatt5]

audio is perfect :)) Thanks so much for the help!

[@TheMathCoach]

@@TheMagicMatt5 thanks! happy to help!

[@hedid4023]

Can you do the abstract vector space please?

[@barsanstefan9506]

This Complex Analysis videos are all insanely good. Crazy how easy you make everything seem. Keep up the good work!

[@TheMathCoach]

Hello Barsan, happy to hear that and happy to help! new video will be out in around 1 - 2 weeks if you want more complex analysis in your life :)

[@DarkMatterSprinkles]

This is by far the best video I've seen when it comes to explaining this. I struggled with a math problem for 3 hours, watched this the first time, and got the right answer before it was over. Thank you! You have done well.

[@rachelcourtney1502]

Showing both proofs and examples are great! Thank you.

[@TheMathCoach]

Glad you liked it! Quite happy with this one!

[@omargaber3122]

Wow ,, What is this wonderful explanation, and what is this wonderful voice!!!!! Amazing scene 🌷

[@TheMathCoach]

Glad you found both the video and my voice helpful :)

[@axelrice7422]

this channel may just save my just teach me everything I should have learned over the past month in time for my test in 2 hours and 5 minutes

[@TheMathCoach]

How did it feel? Hope my channel could help you prepare!

[@minhazulislam4682]

I am really grateful to you man. I missed classes in MAT215(complex variables and la place transformation) and the lecture notes felt out of place. Now I know exactly what my faculty taught us. Thank you, mathcoach.

[@Cav-z1y]

Usually just watch these and do the Q then move on but thought I'd leave a comment, you are fantastic. Thanks

[@chenlingoh6828]

Thank you! It only took me a while to understand it, by far the best video I've seen.

[@TheMathCoach]

Happy to be able to help out! and hey, you got there in the end, good job! :)

[@sfxyz3746]

You should start making video again. This channel should have 100x subscribers. Best math-channel out here

[@sandracordoba6090]

I have been struggling a lot with this topic but your videos are so clear. Thanks for the effort.

[@TheMathCoach]

Glad it was helpful!

[@PunmasterSTP]

Another incredible video, and I am very much hoping to walk way with some residual knowledge!

[@TheMathCoach]

Great job mate, have you watched them all now, or are you saving some for later? I'm still making videos, but for the moment I'm focusing on making a guide to complex analysis (small textbook). If that is something that interest you when consider subscribing to get notifications when it goes live :)

[@tengen011]

I have an exam tomorrow and thanks to you I understand this topic. Great explanation sir !

[@TheMathCoach]

Best of luck on your exam Paeral, happy to help!

[@EamonnO]

Excellent examples - some of the theory is covered in Complex Variables Demystified David McMahon, but not explained as well. The examples filled in some gaps very well.

[@rtydurdu9280]

Would you cover the topics in the textbook of complex analysis by Stein like Poisson summation formula, Weierstrass infinite products, Gamma and zeta function...Those are way more difficult. Definitely need some explanations.

[@TheMathCoach]

Never heard of them before, if you could provide me with some links to the definitions then I might add them to the playlist! But no promises!

[@seiii304]

Your video such a live saver for me, thanks a lot!!

[@TheMathCoach]

Glad it helped!

[@paulmarsh1930]

The examples helped me a lot. Thank you!

[@TheMathCoach]

Glad it helped!

[@gulnazshalgumbayeva8655]

Excellent! I really love and enjoy how you explain

[@TheMathCoach]

Awesome, thank you!

[@diogoprudente6041]

Tysm man. Your channel has all my "análise matemática 3" subjects this helped me Soo much

[@TheMathCoach]

Happy to hear that Diogo! But what is "análise matemática 3" is it the name for the course in your school?

[@diogoprudente6041]

@@TheMathCoach its like calculus 3, I guess. Its the subject about complex analysis. My bet is you are a teacher of calculus 3???

[@TheMathCoach]

@@diogoprudente6041 thanks for the information! this is a hobby of mine which I started when I myself took the course, I have a teacher degree though just not for university.

[@diogoprudente6041]

@@TheMathCoach pls keep making this vids

[@TheMathCoach]

@@diogoprudente6041 editing another video as we speak, will probably be out in a couple of days.

[@HuntBobo]

Examples is same video works better for me. Thanks!

[@TheMathCoach]

happy to hear that, thank you for the feedback!

[@muhamedmuminovic4819]

Thank you so much for all the videos about topics from complex analysis :)

[@TheMathCoach]

I'm happy to help Muhamed, glad to hear that you found my content useful :) gave you access to the pdf right now!

[@tuulipeltola7892]

Best video ever, thank you so much

[@DarkMatterSprinkles]

You explain things really good.

[@Enriquecav]

Your videos are great and very well explained, thank you! - Also I subbed :) -

[@TheMathCoach]

My pleasure to help out! and Welcome to the channel :)

[@SequinBrain]

About proof vs example, the series seems done now, but jic, maybe I haven't reached the point where I can see this yet, but so far, seeing proofs in textbooks doesn't help me figure out how to solve the problems at the ends of the sections. Many texts are very short on examples, but the number & caliber of examples here is at a comfortable level.

[@TheMathCoach]

Thanks for the feedback really appreciate it, it will problably be 2 more videos for the series but there will always be more courses to cover after this one. I will take it into consideration for these ones.

[@SequinBrain]

@@TheMathCoach JIC you have skill in the area, I noticed a dearth in the dept of Real Analysis videos on KZbin. There is one good series. But it seems only a small number of humans can place Real Analysis anywhere in reality to begin with.

[@TheMathCoach]

@@SequinBrain Thank you I will check that out, can you link me to the one playlist you recommend and I will check it out and see if I can bring something more to the table.

[@SequinBrain]

@@TheMathCoach Thanks! Here it is, very good teacher! BUT, this is not only over 10 years old, even though the concepts won't have changed significantly, the video quality is so low that some of the equations are either hard to read or can't be seen. The power of this class from my brief brush with it is the power to prove things, that's an amazing ability once we get it high enough to be reliable. Gluck with whatever you decide. kzbin.info/www/bejne/qaKoqoqCfNupmtk

[@Somethingsomething666]

Hey - Thank you for your work.

[@TheMathCoach]

Hello Chris, I'm happy to be able to help and that all my late night work can be useful for someone else :)

[@psychedelicfungi]

Excellent presentation and explanations! Thank you so much for your videos! One new subscriber :-)

[@TheMathCoach]

Happy to hear that, welcome to the channel psy and let me know if you have any question regarding the content :) best of luck with your studies!

[@padraigfitzpatrick762]

brilliant explanations, thanks

[@kemalbasaran8316]

Excellent! Thanks sir.

[@davidsolooki3051]

Hi! Amazing video! I was wondering why you were able to differentiate 1/z in the last example given that it doesn't satisfy the Cauchy Reimann conditions for z=0? Thanks!

[@TheMathCoach]

Hi, happy to help! can you give me timestamps? since when we apply the residue formula we are doing it while we let z approach one specific value (0 and 1 in this example, depending on the residue) and we do this to avoid dividing with zero. Hope it helps.

[@davidsolooki3051]

@@TheMathCoach Thank you for the quick response! I was referring to the derivative at 8:52. I guess based on your explanation its ok to derive 1/z because we are taking the derivative as z approaches a certain point, (1 in this case). Is that correct? Thank you so much again for all the help and for the great channel!

[@TheMathCoach]

@@davidsolooki3051 yes that is correct! we are avoiding the singularity for that expression so all is fine, welcome to the channel :)

[@claricea5353]

Thank you!

[@TheMathCoach]

I'm just happy to help Clarice and welcome to the channel, let me know if you have any questions about my content and best of luck with your studies :)

[@nima5035]

Thanks a lot for this great video!

[@TheMathCoach]

My pleasure!

[@mortenjrgensen1795]

Very well explained!

[@TheMathCoach]

Glad it was helpful! Thank you Morten :)

[@kafeerojoel8618]

Keep up the good work

[@TheMathCoach]

Thanks, will do!

[@adnanhowlader143]

what if the contour is negatively oriented? do i have to multiply by -1?

[@TheMathCoach]

Yes, it is just a matter of changing the sign. If you change the direction of a path then you have to add a minus sign in front of the integral :)

[@sayajinppl417]

Hey , thanks for the video very clear and helpful , can you please explain in a video this function , The integral of 1/(1+z^6)

[@TheMathCoach]

glad you liked it but sorry I dont take requests right now

[@vikasmeena4822]

Holy 🔥🔥🔥 amazing

[@TheMathCoach]

🔥🔥 Happy to hear that 🔥🔥 Just let me know if you have any questions! The proof will be released this sunday.

[@goldios9300]

just wondering if there is any gaussians integral questions can be solved by residual theroem thank you!

[@TheMathCoach]

Not sure about that, it will simply equal 0 if you don't have any singularites. But there might be such gaussian integrals?

[@princedesperado7787]

I passed my exam because of your videos my friend. Where can I donate some money to at least show my gratitude? Thank you so much!!!!

[@TheMathCoach]

Hi Prince, happy to hear about your stellar results - great job! I want to emphasize that you did all the hard work yourself and I only provided you with some additional resources. All donations are appreciated and I created a PayPal user which I think would be the easiest way: paypal.me/TheMathCoach Have a great day and best of luck with your future studies :)

[@princedesperado7787]

@@TheMathCoach Done! Thank you very much again. P.S. I did not know you are from Sweden :D

[@TheMathCoach]

@@princedesperado7787 you are too kind and yes, you learn something new everyday :)

[@gulnazshalgumbayeva8655]

Can you please create a Videos about conformal maps?

[@TheMathCoach]

Keep going down the playlist and you will find it :)

[@Amani_Rose]

Thank you so much!

[@qinisomaxwellmavuso4178]

Hello guys for the last question Isn't z = 0, z =1, z= -1, since we have a square, or we don't do in that way?

[@TheMathCoach]

Hello, not in this case! if you insert z=-1 then you get (-1-1)^2=(-2)^2 = 4 after taking the square of the parenthesis which is not equal to zero.

[@chensslzz]

Very clear

[@piyushkumarutkarsh9124]

Can't thank you enough.

[@TheMathCoach]

I think you did just fine :) thank you for the kind words!

[@asishcodes]

Thanks

[@TheMathCoach]

Happy to help out!

[@sergiomanzetti1021]

Kanonseminar! Takk!

[@TheMathCoach]

Ibland så, ingen orsak!

[@tiemenjorna6552]

spliddem up

[@TheMathCoach]

what does spliddem means? xD