Mathemaniac | The 5 ways to visualize complex functions | Essence of complex analysis #3 @mathemaniac | Uploaded 3 years ago | Updated 2 hours ago
Complex functions are 4-dimensional: its input and output are complex numbers, and so represented in 2 dimensions each, so how do we visualize complex functions if we are living in a 3D world? There are actually 5 different ways to visualize a complex function, and this video is going to explore a bit about each of them.
Some of you commented that you have already studied complex analysis in full, but hopefully there are still some things that you haven't seen before, because a typical university course on complex analysis wouldn't contain as many visuals as seen in this video.
I know this might not be recommended by YouTube as much simply because the video is not that long (less than 20 minutes), and it seems like YouTube only puts my videos in recommendations when my video is very long. Originally I wanted to put things that will be covered in the next video into this particular video, but I figured that it doesn't make sense to cram two quite separate things into one video just for the sake of watch time. So please consider sharing this video, liking and commenting so that more people can watch it!
LEARN A LITTLE BIT MORE HERE:
More about complex visualisation: http://www.nucalc.com/ComplexFunctions.html
Joukowsky transform: complex-analysis.com/content/joukowsky_airfoil.html
Joukowsky transform (NASA): grc.nasa.gov/www/k-12/airplane/map.html
Credits to Yehuda, there is an interactive tool to obtain the domain colouring plot for complex functions here: https://people.math.osu.edu/fowler.291/phase/
Music used:
Heavenly - Aakash Gandhi
from YouTube audio library
Video chapters:
00:00 Introduction
01:03 Domain colouring
03:35 3D plots
05:45 Vector fields
07:50 z-w planes
10:53 Riemann spheres
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
Social media:
Facebook: facebook.com/mathemaniacyt
Instagram: instagram.com/_mathemaniac_
Twitter: twitter.com/mathemaniacyt
Patreon: patreon.com/mathemaniac (support if you want to and can afford to!)
For my contact email, check my About page on a PC.
See you next time!
Complex functions are 4-dimensional: its input and output are complex numbers, and so represented in 2 dimensions each, so how do we visualize complex functions if we are living in a 3D world? There are actually 5 different ways to visualize a complex function, and this video is going to explore a bit about each of them.
Some of you commented that you have already studied complex analysis in full, but hopefully there are still some things that you haven't seen before, because a typical university course on complex analysis wouldn't contain as many visuals as seen in this video.
I know this might not be recommended by YouTube as much simply because the video is not that long (less than 20 minutes), and it seems like YouTube only puts my videos in recommendations when my video is very long. Originally I wanted to put things that will be covered in the next video into this particular video, but I figured that it doesn't make sense to cram two quite separate things into one video just for the sake of watch time. So please consider sharing this video, liking and commenting so that more people can watch it!
LEARN A LITTLE BIT MORE HERE:
More about complex visualisation: http://www.nucalc.com/ComplexFunctions.html
Joukowsky transform: complex-analysis.com/content/joukowsky_airfoil.html
Joukowsky transform (NASA): grc.nasa.gov/www/k-12/airplane/map.html
Credits to Yehuda, there is an interactive tool to obtain the domain colouring plot for complex functions here: https://people.math.osu.edu/fowler.291/phase/
Music used:
Heavenly - Aakash Gandhi
from YouTube audio library
Video chapters:
00:00 Introduction
01:03 Domain colouring
03:35 3D plots
05:45 Vector fields
07:50 z-w planes
10:53 Riemann spheres
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
Social media:
Facebook: facebook.com/mathemaniacyt
Instagram: instagram.com/_mathemaniac_
Twitter: twitter.com/mathemaniacyt
Patreon: patreon.com/mathemaniac (support if you want to and can afford to!)
For my contact email, check my About page on a PC.
See you next time!
