5 ms·

Overview of differential equations [video]

273 points by espeed 8y ago

scranglis 8y ago
If you're excited to actually do some problems by the end of the video, we just released our diff. eq. problem solving course: https://brilliant.org/courses/differential-equations/ https://brilliant.org/courses/differential-equations/
- mathnmusic 8y ago
  Thank you. I have added both of these links to learn-awesome's calculus page: https://github.com/learn-awesome/learn-awesome/blob/master/calculus.md https://github.com/learn-awesome/learn-awesome/blob/master/c...
  - scranglis 8y ago
    Neat!
- mykowebhn 8y ago
  What do you think of sponsoring 3b1b instead of advertising for free here?
  - pixelperfect 8y ago
    They actually have sponsored 3b1b in the past.
  - scranglis 8y ago
    We have in the past! And we'd love to in the future. However, Grant doesn't need sponsors any longer since his Patreon is healthy, which is awesome.
  - glandium 8y ago
    3Blue1Brown went sponsor-free recently: https://www.patreon.com/posts/19586800 https://www.patreon.com/posts/19586800 Discussed here: https://news.ycombinator.com/item?id=17639322 https://news.ycombinator.com/item?id=17639322
ricardbejarano 8y ago
I just want to thank 3b1b, and tell anyone who's trying to get in love with math to go ahead and binge his channel. I've been terrible at math since they started to get "hard" as a teenager, which then compounded into not liking math before and after getting into college for a CS degree. The degree inevitably requires some math background at the beginning, so I struggled with that a lot, until I discovered 3b1b. His series on calculus and linear algebra got me through both subjects in less than a week. From 0 to 7 in the scale of 0 to 10 we use in my university, in just 3-4 days per subject. I regret not discovering it before. What those two series helped me with was understanding why math is important, and how can one solve everyday problems with math, which is something teachers say when you are young but don't actually tell. Realising that instantaneously motivated me to put in time and effort, which is key when learning math. The machine learning series also helped me find the answer to the "why am I learning math if I'm just a tech?" question. On the side, I'm now reading "Computer Networking: a Top-Down Approach" by Kurose, which made me get to the conclusion that we are teaching things wrong. The educational system that brought me here teaches you on a promise of everything making sense once you understand it all, which makes it really hard to understand the pieces in the first place. The book takes a different approach in that it shows you the final result, and then breaks it down abstraction by abstraction, which makes you eager to know what's going on behind the next abstraction. If I were to teach a kid how a mechanical watch works, I wouldn't start by the gears, I'd start by the watch itself, and then break it down piece by piece. Once he knows that there's this abstract system that takes some force in one end, and spits some other force in the other, then the kid will want to know what's behind the abstract system, and he'll be ready to know it. This way I'll keep the attention of the kid till the end, instead of telling him "you'll understand once we finish" after each lesson.
- selimthegrim 8y ago
  I’ve seen that book on the shelf of a friend of mine at MSR and I wasn’t sure why. Now I’ll be sure to check it out.
  - ricardbejarano 8y ago
    It's a great book, I'm reading it to reinforce those low-level knowledge gaps that appear when you're self-taught. I discovered here: https://teachyourselfcs.com/ https://teachyourselfcs.com/, I've bought some other books listed there.
monochromatic 8y ago
3blue1brown has some of the best math exposition I’ve ever seen. I’m consistently impressed with his videos.
dan-robertson 8y ago
Looking at phase diagrams is something that feels weird at first but turns out to be very nice. I think one reason it’s weird is that (when one follows the normal track of education through school and into a degree like physics or mathematics at university), this is the first time (at least in th uk school system) when one stands basically no chance of actually solving the equations but giving good useful qualitative information about the solutions is possible. I think part of why it can be hard to learn is that one must guess what is in the unknown areas whereas in past problems with limited information (eg in geometry), the puzzle is to derive just enough information on the boundary to solve the problem, so one may not be able to say something about the areas of some figures but might have something to say about their sum. I found the trick to phase diagrams was realising that they are mostly made of a few interesting features: at every fixed point the diagram is some combination of a circular motion and a scaling in/out motion, or it is some kind of saddle point going out in one direction and in at another (eg the fixed point at the top of the pendulum in the video). Then you just fill in the gaps. This feels hard at first because you can imagine there could be anything in the gaps but it is actually easy because the flow lines do not cross and one cannot have significant turbulence without fixed points (and those have all been found) so only boring things can be drawn in the gaps. The same is also true with drawing contour diagrams, just replace fixed point with stationary point, and flow line with isosurface.
mindcrime 8y ago
If you want to dig even deeper into diffeq, Professor Leonard has been publishing his series[1] on the topic over the past few months. He's up to lesson #31 so far.. not sure how many total the series is supposed to be. [1]: https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_ https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKV...
nQueens 8y ago
Endless intellect seeking, and yet whatever shall it amount to? Navel gazing? Trophy collecting the smartest asses you can put in your chairs? Yes you have a smart person in your clutches, and they give over to the psychological domination of the paycheck, and so now, sooner or later, with enough smart people in the same room, like oily rags drying in the hot sun, surely something will catch fire. Watch it all evaporate and amount to nothing. Never meet the fundamental needs. The ones that matter, and never fail to be surprised at the rest.
29athrowaway 8y ago
The library used for the animations: https://github.com/3b1b/manim https://github.com/3b1b/manim Sources for episodes are included: https://github.com/3b1b/manim/tree/master/active_projects/ode/part1 https://github.com/3b1b/manim/tree/master/active_projects/od... The composer behind for many of the songs is Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://vincerubinetti.bandcamp.com/album/the-music-of-3blue... 3b1b interview: https://www.youtube.com/watch?v=A0RH93XvSyU https://www.youtube.com/watch?v=A0RH93XvSyU

273 points by espeed 8y ago

If you're excited to actually do some problems by the end of the video, we just released our diff. eq. problem solving course: https://brilliant.org/courses/differential-equations/ https://brilliant.org/courses/differential-equations/

mathnmusic 8y ago
Thank you. I have added both of these links to learn-awesome's calculus page: https://github.com/learn-awesome/learn-awesome/blob/master/calculus.md https://github.com/learn-awesome/learn-awesome/blob/master/c...
- scranglis 8y ago
  Neat!
mykowebhn 8y ago
What do you think of sponsoring 3b1b instead of advertising for free here?
- pixelperfect 8y ago
  They actually have sponsored 3b1b in the past.
- scranglis 8y ago
  We have in the past! And we'd love to in the future. However, Grant doesn't need sponsors any longer since his Patreon is healthy, which is awesome.
- glandium 8y ago
  3Blue1Brown went sponsor-free recently: https://www.patreon.com/posts/19586800 https://www.patreon.com/posts/19586800 Discussed here: https://news.ycombinator.com/item?id=17639322 https://news.ycombinator.com/item?id=17639322

ricardbejarano 8y ago

I just want to thank 3b1b, and tell anyone who's trying to get in love with math to go ahead and binge his channel. I've been terrible at math since they started to get "hard" as a teenager, which then compounded into not liking math before and after getting into college for a CS degree. The degree inevitably requires some math background at the beginning, so I struggled with that a lot, until I discovered 3b1b. His series on calculus and linear algebra got me through both subjects in less than a week. From 0 to 7 in the scale of 0 to 10 we use in my university, in just 3-4 days per subject. I regret not discovering it before. What those two series helped me with was understanding why math is important, and how can one solve everyday problems with math, which is something teachers say when you are young but don't actually tell. Realising that instantaneously motivated me to put in time and effort, which is key when learning math. The machine learning series also helped me find the answer to the "why am I learning math if I'm just a tech?" question. On the side, I'm now reading "Computer Networking: a Top-Down Approach" by Kurose, which made me get to the conclusion that we are teaching things wrong. The educational system that brought me here teaches you on a promise of everything making sense once you understand it all, which makes it really hard to understand the pieces in the first place. The book takes a different approach in that it shows you the final result, and then breaks it down abstraction by abstraction, which makes you eager to know what's going on behind the next abstraction. If I were to teach a kid how a mechanical watch works, I wouldn't start by the gears, I'd start by the watch itself, and then break it down piece by piece. Once he knows that there's this abstract system that takes some force in one end, and spits some other force in the other, then the kid will want to know what's behind the abstract system, and he'll be ready to know it. This way I'll keep the attention of the kid till the end, instead of telling him "you'll understand once we finish" after each lesson.

selimthegrim 8y ago
I’ve seen that book on the shelf of a friend of mine at MSR and I wasn’t sure why. Now I’ll be sure to check it out.
- ricardbejarano 8y ago
  It's a great book, I'm reading it to reinforce those low-level knowledge gaps that appear when you're self-taught. I discovered here: https://teachyourselfcs.com/ https://teachyourselfcs.com/, I've bought some other books listed there.

monochromatic 8y ago

3blue1brown has some of the best math exposition I’ve ever seen. I’m consistently impressed with his videos.

dan-robertson 8y ago

Looking at phase diagrams is something that feels weird at first but turns out to be very nice. I think one reason it’s weird is that (when one follows the normal track of education through school and into a degree like physics or mathematics at university), this is the first time (at least in th uk school system) when one stands basically no chance of actually solving the equations but giving good useful qualitative information about the solutions is possible. I think part of why it can be hard to learn is that one must guess what is in the unknown areas whereas in past problems with limited information (eg in geometry), the puzzle is to derive just enough information on the boundary to solve the problem, so one may not be able to say something about the areas of some figures but might have something to say about their sum. I found the trick to phase diagrams was realising that they are mostly made of a few interesting features: at every fixed point the diagram is some combination of a circular motion and a scaling in/out motion, or it is some kind of saddle point going out in one direction and in at another (eg the fixed point at the top of the pendulum in the video). Then you just fill in the gaps. This feels hard at first because you can imagine there could be anything in the gaps but it is actually easy because the flow lines do not cross and one cannot have significant turbulence without fixed points (and those have all been found) so only boring things can be drawn in the gaps. The same is also true with drawing contour diagrams, just replace fixed point with stationary point, and flow line with isosurface.

mindcrime 8y ago

If you want to dig even deeper into diffeq, Professor Leonard has been publishing his series[1] on the topic over the past few months. He's up to lesson #31 so far.. not sure how many total the series is supposed to be. [1]: https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_ https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKV...

nQueens 8y ago

Endless intellect seeking, and yet whatever shall it amount to? Navel gazing? Trophy collecting the smartest asses you can put in your chairs? Yes you have a smart person in your clutches, and they give over to the psychological domination of the paycheck, and so now, sooner or later, with enough smart people in the same room, like oily rags drying in the hot sun, surely something will catch fire. Watch it all evaporate and amount to nothing. Never meet the fundamental needs. The ones that matter, and never fail to be surprised at the rest.

29athrowaway 8y ago

The library used for the animations: https://github.com/3b1b/manim https://github.com/3b1b/manim Sources for episodes are included: https://github.com/3b1b/manim/tree/master/active_projects/ode/part1 https://github.com/3b1b/manim/tree/master/active_projects/od... The composer behind for many of the songs is Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://vincerubinetti.bandcamp.com/album/the-music-of-3blue... 3b1b interview: https://www.youtube.com/watch?v=A0RH93XvSyU https://www.youtube.com/watch?v=A0RH93XvSyU