
Overview of differential equations [video] - espeed
https://www.youtube.com/watch?v=p_di4Zn4wz4&list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6&index=2&t=0s
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ricardbejarano
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.

~~~
arendtio
Well, I think there is some deeper truth to 'everything making sense once you
understand it all'.

Granted, it doesn't really work as a motivator and those who use it as such
are missing a real motivator quite often. Nevertheless, when you think about
people, you will find that their actions will make sense once you see all the
factors that influence them. Knowing that you probably don't know all factors
that affect a person's actions will make you search for the missing parts
before judging that person, resulting in a suspension of judgment [1] which is
quite valuable actually (not just for human interactions).

[1]
[https://en.wikipedia.org/wiki/Suspension_of_judgment](https://en.wikipedia.org/wiki/Suspension_of_judgment)

~~~
ricardbejarano
Yeah but losing a kid's motivation is terrible. Having a kid eager to know
what's next means the kid will think about it on the commute home, talk about
it with his/her parents, ask some hard questions... He/She will be _curious_.

And curiosity is the greatest of all drives. I've spent more hours than I can
count following curiosity with no other prize but knowledge. Instead, we've
come to tell kids that they should memorise this thing for the next week, and
move on.

For a given concept, with three layers of abstraction, if we start bottom-up,
with the downmost layer, the kid doesn't know what that layer's good for. That
happens until we get to the topmost layer. The layers have no purpose until
we've finished 4 months from now. They don't make sense.

If you teach kids backwards, once the kid knows the topmost layer, he/she will
know what the next layer is good for and in what conditions shall it exist.
The _next layer_ has a purpose, which the kid can understand and expect.

The Socratic method works this way. You start with the general purpose of the
system, and then you break it down question by question.

(teacher)- What is this?

(student)+ This is a car.

\- What is a car good for?

\+ It moves people.

\- How does it move people?

\+ Because it moves these wheels.

\- How does it move those wheels?

\+ Because... I don't know (takes a car replica), it has these bar connected
to those wheels, and this other bar connected to that bar.

\- What happens when you spin that second bar?

\+ The wheels move.

\- So to move the car, you move those wheels, and to move those wheels you
spin this bar, but you don't manually spin this bar when you are driving, who
does so then?

\+ I don't know.

Now the kid is ready to understand what an engine is.

If we did it backwards, and started with combustion, the kid would have no
idea what combustion is for until we've reached the car.

~~~
meko
I for one am super in favor of the top-down approach of teaching. Amused
because it's similar to how a song is written, or a painting is done: big
broad strokes, working forward to then fill in the subject and details

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scranglis
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/)

~~~
mykowebhn
What do you think of sponsoring 3b1b instead of advertising for free here?

~~~
scranglis
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.

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dan-robertson
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.

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mindcrime
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=PLDesaqWTN6ESPaHy2QUKV...](https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_)

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29athrowaway
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/od...](https://github.com/3b1b/manim/tree/master/active_projects/ode/part1)

The composer behind for many of the songs is Vincent Rubinetti:
[https://vincerubinetti.bandcamp.com/album/the-music-
of-3blue...](https://vincerubinetti.bandcamp.com/album/the-music-
of-3blue1brown)

3b1b interview:
[https://www.youtube.com/watch?v=A0RH93XvSyU](https://www.youtube.com/watch?v=A0RH93XvSyU)

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

