Differential equations, a tourist's guide | DE1

An overview of what ODEs are all about
An equally valuable form of support is to share the videos.

Error correction: At 6:27, the upper equation should have g/L instead of L/g.

Steven Strogatz's NYT article on the math of love:

Interactive visualization of the example from this video, by Ilya Perederiy:

If you're looking for books on this topic, I'd recommend the one by Vladimir Arnold, "Ordinary Differential Equations"

Also, more Strogatz fun, you may enjoy his text "Nonlinear Dynamics And Chaos"

Curious about why it's called a "phase space"? You might enjoy this article:

From a response on /r/3blue1brown, here are some interactives based on examples shown in the video:

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Vietnamese: @ngvutuan2811

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If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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Various social media stuffs:

[bluebrown]

Some notes on the intended use of this series. I was deliberate in using the phrase "tour of differential equations", as opposed to "introduction to" or "essence of". I think of the relationship between watching this series and taking a course as being analogous to the relationship between touring a city vs. living in it. You'll certainly see a lot less with the tour since you're spending less time overall, but the goal will be to walk around some of the most noteworthy monuments and town centers with helpful context given to you by a guide. And just as someone who lives in a city may very well have never gone to visit some of the historical sites of their town, despite living there for years, many differential equations students may not always get the chance to zoom out and appreciate the central cornerstones of the subject amidst all the computations they are learning.


I hope you enjoy the tour, but at the same time know that it is, by design, very different from taking courses on the subject.

[Alexander_Sannikov]

I basically solve all kinds of differential equations for living: modelling soft body dynamics, rigid body dynamics, optics, whatever. I just wanted to give an advice to anyone aspiring to learn all this stuff. What they often teach you at school/uni is how to solve these equations analytically : sure, this is sometimes useful. However, in most real applications, it's more productive to be able to write a program to solve them rather than to do that "manually". Even the simplest explicit solver that's literally 2 lines of code, instantly covers 95% of all differential equations, even though its performance and accuracy are not the best. It's kind of a brute force solution.


One might even start thinking that "hey, if my computer can just solve all these equations, why even bother studying them?". And the reason is very simple: by applying knowledge of certain types of DE's and by using more advanced solvers, one can increase performance and accuracy of these solvers by orders of magnitude. Which might make a huge difference: physics simulation in your game becomes more stable, your rendering algorithm can run your effects 60fps instead of 5fps, you can render your image in higher resolution on the same hardware, etc. My idea is, don't think of your computer as a replacement for your knowledge. Think of it as of an incredibly powerful tool, that still fully depends on your skill.

[zsoltlendvai]

, ,To be realistic, let’s add air resistance”. All of my phisics books in my life: we don’t do that here.

[ewin]

I am a math major, and have taken classes in both ODEs and partial differential equations, and I still find my mind being blown at how this field is so important

[nickm]

3B1B making differential equations videos? Two years of optimistic dreams have reached fruition!
Thank you so much. The amount your videos help visualise and truly understand concepts is incredible.

[ColoredScreens]

I had no idea we could model "playing hard to get" with differential equations, but you did it quite elegantly! Bravo!

[HalcyonSerenade]

Most 3B1B videos:

- Average viewer: "math is hard"
- 3B1B: "Well, look at it like this and it's not so bad."

This 3B1B video:

- Average viewer: "math is hard"
- 3B1B: "yea u rite, but look at it like this anyway"

[jorgegutierrez]

Grant, I doubt you will read this (I know from your Numberphile interview that you don’t read these so much anymore), but you are just an amazing presence in my life.

You are a teacher to me of the highest caliber but most importantly, you awakened a love of math and physics in me. You are part of the reason why I am getting through college and why I decided to do Applied Math and Computer Science.

God bless you and in everything you will do in the future. You are a master of your craft.

[aleksanderboci]

I understood about 15% of what i saw, but i loved every single second of it. Great work!

[mesharial]

*just finished an ODE class and I don't wanna look at another DE again in my life*


me: oh 3blue1brown video about DE *click*

[garnetedinger]

I'm taking an engineering course on differential equations and this is super helpful. My teacher gets so caught up in the specifics of methods that it's hard to understand the applications for what each term actually represents. This video is an excellent complement to the course in actually understanding what I'm learning. Keep up the great work!

[zelllers]

THIS IS THE BEST SUNDAY IVE HAD IN WEEKS.


Every single teacher I've ever had in my life has failed to make me excited about math (except for one of my physics teachers, but I think that was more because I was seeing math applied for the first time than anything). YOU have made me more excited about learning these abstract ways of thinking than anyone else in the entire world.


Thank you

[erikziak]

There should be a Nobel prize for YouTube videos and this channel should be the first one to win it!

[biblicallyaccurateangel]

i honestly understand none of this as a freshman in highschool, but i put 3blue1brown videos on while working on essays because it helps me get into the writing mood, and its so relaxing. i love this dude’s vibe, it’s so chill and you can tell he really loves making these videos.

[Jeffrey_Wong]

My 8th grade math teacher insisted that math was beautiful. I didn't understand what she meant until I started watching your videos.

[isaac]

Diff eq was a nightmare, I regurgitated info, got a bad grade, and forgot everything. I was so apathetic to the entire class, I just didn't give a damn about any of it. Now I have the ability to actually get a deeper understanding of the class I spent God knows how much money for.
Thank you.

[amrrelsheikh]

I'm speechless about the beauty of this video. I want to become a mathematician now.

[miguelcamargo]

Hopefully this will explain Laplace transformations better than how I understand it now.

[EntropicalNature]

Being a math teacher myself, I truly feel humble. By far the best math visualizations in combination with a concise way of delivering abstract concepts available on YouTube! Thanks so much 3Blue!

[tielessin]

*A couple goes to a consultation
Couple: "So it's always going up and down in our relationship"
Grant: "How familiar are you with differential equations?"


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