Complex Analysis 1 | Introduction

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This is my video series about Complex Analysis. I hope that it will help everyone who wants to learn about complex derivatives, curve integrals, and the residue theorem. Complex Analysis has a lof applications in other parts of mathematics and in physics.

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00:00 Introduction
02:13 What we need
03:18 Metric space
04:43 Sequences and convergence in ℂ
07:32 Continuity for complex functions
09:30 Endcard

#ComplexAnalysis
#Analysis
#Calculus
#Mathematics
#curveintegral
#integration

(This explanation fits to lectures for students in their first or second year of study: Mathematics, Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[brightsideofmaths]

Please do the quiz to check if you have understood the topic in this video:

[umbranocturna]

This could be a lifesaver, very unhappy with my current lectures.

[alacaleb]

My stress in maths are finally over. Thanks for the video

[barrybai]

I needed this 2 months ago! Great material!

[malawigw]

Finally! One of my fav subjects in math :) Been more than 10 years since I studied it, looking forward to recap some of the stuff here :) Happy new year!

[alute]

I swear your videos could literally bring me to a new higher order realms of being High!
Danke

[arunjayaraman]

I wish I discovered your series while taking Real Analysis. But it is okay because now I watch your videos for fun! By the way, what software do you use to make and draw over your videos?

[ZanderzMcCluer]

I've been wanting to learn more about complex analysis for years now! My college campus sadly has no courses in this. Thank you so much!!!!

[Duskull]

If only this playlist was made 2 semesters ago T_T
I'll be sure to watch it when i retake this course to improve my grade in the near future :)

[ezzaddin]

Hey dude you are doing gods work here. I am in highschool and your explanations could not be more clear. Much thanks!

[joshuad.furumele]

I'm about to start my third yr in a couple of weeks, and I was so apprehensive about which modules to pick, especially Complex Analysis coz it sounded scary... But you made it sound so interesting, and it felt like a natural continuation of Real Analysis which was fun for me. Thank you. If I had any money I would defs support your channel💕

[josephatmbuya]

please help me solve this:

find the cube root of the complex number z=-1+i

[thesorrowfulhero]

*Holomorphic functions, Cauchy-Riemann equations, integration, zeroes of analytic functions, Cauchy
formulas, maximum modulus theorem, open mapping theorem, Louville’s theorem, poles and sin-
gularities, residues and contour integration, conformal maps, Rouche’s theorem, Morera’s theorem*. These are some topics I'd love to see being covered in this course. Thank you for making this series 🙏🙏

[akrishna]

Happy new year! I was just checking your channel after having found it recently to see if you had any lectures on the subject, really excited to see this series from you!

[PunmasterSTP]

Introduction? More like "Unmitigated instruction!" This lecture was jam-packed with information, and I loved watching every second of it. Thanks for making and uploading these wonderful videos!

[pinklady]

*HAPPY NEW YEAR.*

Thank you for continually making videos.

[NewDeal]

Your videos are among the best on the Youtube simply for the reason you take time to motivate the definitions and provide clear examples of their use and concstruction. That really shows the vast majority of difficulties for students learning math lies not only in how complicated the ideas are, but in how poorly the subject is handled. Waiting forward with great anticipation!

Btw, do you think it'd be useful to get some inspiration from Rudin and begin using topolog-ish terms like compactness, perfectness etc. to simplify the theorems and properties in the long run? What is your view on that!

Have a wonderful year, thanks for all the content!

[gutzimmumdo]

do you cover the residue theorem in this course? thanks

[realAhmedAbdElGhany]

waiting for this to complete, that's so awesome i can't even believe my eyes, please keep going !!!

[stephenkormanyos]

Superb. Concise and straight forward foundational presentation. I wish I had your videos when I studied math 25 years ago.
Cheers!
Steve K.