Differential Equations: The Language of Change

[@ArtemKirsanov]

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/ArtemKirsanov . You’ll also get 20% off an annual premium subscription

[@NewDeal1917]

This surely belongs to the top-5 list of youtube videos ever made on the subject, makes you truly accept how a man driven with pure enthusiasm and determination can outperform the entire university departments when it comes to teaching.

[@quecojonesq]

I love you man, please keep at it. I cannot stress enough how useful and informative your videos are. You deserve the world for this work.

[@ArtemKirsanov]

Thank you! Really appreciate it ❤️

[@leif1075]

​@@ArtemKirsanovYes thanks for sharing but I hope you can respond to my other comment when you can Artem. Thank you much.

[@Gome.o]

I don't know what exactly you did differently in this video, but it's working. Normally I find the concepts you discuss too hard to follow and then end up clicking off the video. This time I was engaged all the way through. This is great content! Keep it up 🙂

[@bhaveshsuthar4423]

Learned yesterday about Hopfield networks from ur video. And today John Hopfield & Geoff Hinton wins 2024 physics Nobel prize. Keep making in-depth videos on such topics Artem, they’re very intriguing.

[@macchiato_1881]

Your video on dendritic systems inspired me to study about neuromorphic computing, and then reservoir computing, and as an extension, dive deep into DEs and dynamical systems. It feels weird how the rabbit hole that started me on my journey has caught up to me 😅😅

[@joeystenbeck6697]

I'd love to see a node graph that shows a bunch of people's paths and see how similar they are. All living things strive for their source I guess haha

[@6AxisSage]

​@@joeystenbeck6697have a look at my geocog sims, i have one that models people

[@macchiato_1881]

@@joeystenbeck6697 I'd even go as far to say that it's a sort of dynamical system with attractor points lol. Similar people ofter gravitate towards similar interests

[@joeystenbeck6697]

Good point. Just don't analyze it *too* much or you'll accidentally do the observer effect on the whole universe and collapse reality into a single one or zero 😂 I hope we score a point

[@6AxisSage]

@@joeystenbeck6697 wait whats this? i dont want to that.. is that why people cant process my stuff.. stops the universe breaking?

[@maksimrakhman]

Thanks!

[@Tom-sp3gy]

This is the best channel on computational neuroscience ever!

[@pavlovsdawg]

doing brilliant work spreading the beauty of computational neuroscience as always. as a physics major doing comp-neuro research, your videos synthesize topics in math, physics, and biology together very well and are a must watch for any who seek a deeper understanding of electrophysiology and neural networks. perhaps the next hopfield is a member of this lovely community :)

[@ArtemKirsanov]

Thank you so much!

[@arj123sub]

Great video. You rekindled my interest to restart studying differential equations.

[@ismailhasan348]

The astounding visuals makes the video hundred times more interesting. Love your work.

[@xXCindellaXx]

Underrated chanel, love to hear that more is coming up

[@Abe-qu9tl]

I powered through dif eq in college just to get the job. And now you’re really teaching me to know what I do rather than to just do the math cuz I know the formulas.

[@SayandipRoy-n7j]

Wow so amazing explanation mind blowing !!!

[@varunahlawat9013]

Definitely deserved an immediate subscribe!!

[@Sam-eo2ky]

im a simple man: i see an Artem Kirsanov video and i click...s/o you the goat man!

[@rlcircuit]

Thank you for making these videos! You really made difficult concepts easy to understand. Bravo!

[@yashwantherukulla4122]

where were you 4 months agoooo 😭😭I really needed this vid for a course in my previous semester. thnx for making and as always excellent quality! I hope nothing but the best happens to you 😄

[@neurosciencebeyond]

I just discovered your channel, and it's remarkable! The explanations are so smooth, and the graphics are fantastic. I'd love to learn more about how you create them!

[@eddielally2045]

@@neurosciencebeyond i think he has a video explaining his process

[@douglasstrother6584]

I first got turned-on to this stuff when studying the Duffing Oscillator in my Classical Mechanics class. Dynamical Systems put the WOW! back into Physics for me.

[@animal_expert]

You're an amazing teacher. This was very insightful, well-structured, and wonderfully presented. Reminds me of 3B1B. Keep it up!

[@foreverjoyous]

Awesome stuff! Would love to see how this can be used to visualize recurrent neural network activity!

[@6AxisSage]

@@foreverjoyous u can see how recurrent information loops work in cortical columns in some of my simulations

[@Viewpoint314]

Very nice and clear presentaion.

[@kikumayumi9219]

Beautifully simple yet perfectly explained

[@wintg931]

Babe wake up, the new video from Artem Kirsanov has been released.

[@cryingsurrogate]

Thanks babe

[@carlossegura403]

cringe

[@kingki1953]

​@@carlossegura403r/whooosh

[@neologicalgamer3437]

Hey, what's your pfp from?

[@Impaled_Onion-thatsmine]

And schizophrenia within philosophy of the mind

[@BlueBirdgg]

Beautiful. This is incredible! Thanks a lot. Solve a lot of things in my mind!

[@lunafoxfire]

These videos are consistently amazing! Very excited for the next in the series! Getting into the actual math/dynamics of a neuron seems _extremely_ fascinating!

[@DavidoulaGeorgopoulou]

This is truly amazing! I think you can make almost everyone love mathematics and neuroscience through your videos:))

[@gman5454]

Brother you have a knack for this. Keep up the good work, love your videos 👍🏻

[@dan_pal]

Impecable explanation, as expected from Artem. Thanks for another great video

[@arandomdiamond2]

Looking forward to the next video! PS. 12:44 minor issue in definitions? x dot is change in population.

[@peacekeeper9687]

Great quality educational video. 👍

[@jtr1234]

What’s great video!! Differential equations is the most interesting thing to understand and you do an amazing job!!

[@luissantiago4768]

Excellent video!!!

[@mattthelearner2797]

I’m sharing your channel to everyone I know… Come on guys we need Artem’s channel to grow!

[@KathySierraVideo]

I live on an island with no foxes (or other rabbit predators) and the rabbit numbers becomes overwhelming, but then every few years a rabbit virus wipes out nearly the entire island’s rabbit population. It’s both a relief to us (farmers) and terrifying to see literally thousands of rabbits on the island all drop dead within a few days. So, yeah, other variables in a dynamical system 🤷🏼‍♀️.

[@peteintania]

Looking forward to the next video!

[@youMatterItDoesGetBetter]

Artem > College. (I got my piece of paper, but school is so outdated).

[@АртурИванов-ч9э]

Артём, у тебя великолепный канал 👏 все лучше и лучше! Рад снова тебя увидеть

[@ctwz71]

Thanks for the class, professor Kirsanov. You have didactics!

[@PeredurJenkins]

Thanks for making this!

[@zacharyboschbird]

This is so intuitive youre hella creative

[@megh_d_aout]

great work Artem ! keep going :)

[@watcheroffunnystuff]

Your channel is of such a high quality, I hope to be able to convey my ideas with such skill one day.

[@maksimrakhman]

Brilliant, thank you! NY finest!

[@veniasblack]

Loved how he simplifies the topic to be suitable for people who have no stomach for math. Is there any book recommended to study differential equations in the same way he did?

[@tharunragumar8008]

THANK YOU BRO

[@godfreypigott]

An English tip: in English we don't say "our today's video".. Not sure if you're German, but German's "unser heutiges Video" doesn't translate directly into English. You would just say "today's video", or perhaps "our video today".

[@mathforai-j5y]

very good explanation

[@atommax_1676]

Feeling kinda proud that I knew all math in the video in my 16, and also reminded that I haven't studied DE for a few month already. Your videos are amazing, i find answers for exact questions that bothered me for a long time. Thank you

[@ct---cp8li]

🤣I am even prouder I knew them all when I was 13

[@GEMSofGOD_com]

Велиуолепный контент бро, как всегда. Топ-1

[@pauljones9150]

Wow! 😲 Never knew about limit cycles

[@Alan-gj5xe]

Extremely good Video I would love some Future Videos about more biological Applications

[@vffuunnyy]

Spasibo za video 😉

[@CopperKettle]

Thank you, this is quite interesting, as always

[@mynamesgus4295]

your videos are amazing thank you for the content

[@TiborVass]

Keep these gems coming! Can't wait to watch your next videos!

[@Determine-gc6sq]

You should do a video on neurophysiology: I would love to learn why neurons and large interconnected sets of neurons cause certain effects. Like why does a biological neural network cause act x rather than act y? We know that neurons depolarize and hyperpolarize, and are numerous in amount and also amount of synapses, and we know that there are certain structures and regions and pathways in BNNs, but ultimately how/why does act x occur rather than act y? That's a question that I am extremely interested in and really want to determine the answer to.

[@waff6ix]

LOVE THESE VIDEOS 💯🤩🤩

[@abook1991]

Your graphs are so pretty! What visualization tool are you using for your phase portraits?

[@ArtemKirsanov]

Thanks! Just vanilla matplotlib quiver + a little After Effects magic for glow effects 😅

[@ambassador_in_training]

Благодарю Артём. Мне очень понравилось твоё объяснение дифференциальных уравнений и как они помогают понимать мир вокруг нас.

[@ArtemKirsanov]

Спасибо! ❤

[@alexandre.c.andreani]

underrated channel

[@TavoLL1511]

I remember having a lot of problems understanding the concept of phase space due to my professor being terrible explaining it when I took the dynamical systems class. But your explanation was infinitely more clear and perfectly understandable. After seeing some of your videos I can honestly say you're one of the best science youtubers out there.

[@fallenangel8785]

i love this channel

[@egoredmc]

Классные видео и крутая тема для видео! Подозреваю, что в следующий раз тема видео уйдёт куда-то в бифуркации и это будет крайне интересно Кроме того, было бы занятно почитать, над чем ты работаешь, если есть такая возможность

[@SilentderLaute]

Another great video :)

[@ArtemKirsanov]

Thanks!

[@hotmole7621]

beautiful video

[@mathforai-j5y]

very informative, please keep doing this💞💕💓💗❣💯❤💯💯💯💯💯💯💯

[@0xdtt11]

Where can I learn it more ? Like a formal online course or something .

[@GamerMeth4]

excellent!!

[@seille3774]

Amazing video Artem. I did Economics and Applied Maths in University, and I chose Economics. Now I'm coming back to Applied Math, because i want to learn to solve complex problems. Any suggestions for software I can use to create and visualise models with as you did in this video? Thanks

[@fungus3329]

MATLAB

[@MeInsideTheBox]

Great video overall, but limit cycles are technically defined differently. What you showed is just oscillatory behavior. Limit cycles happen when different phase space paths converge onto a cycle, as opposed to a single point. This isn’t possible in two dimensions, which is maybe why you didn’t show it, but a disclaimer would have been nice.

[@lunafoxfire]

I think a limit cycle actually is possible in two dimensions. But I think you are right that a truly exactly periodic system would not technically be a limit cycle, since limit cycle implies that other paths tend to converge to it. And the population system is made up of infinitely many "shells" that don't transition between each other. Which maybe you could consider to be infinitely many limit cycles, depending on your definitions?

[@90800905675]

You're correct that these are indeed no limit cycles, however limit-cycles in 2-dimensional phase space are certainly possible (see, e.g., Van der Pol oscillator)

[@4thpdespanolo]

I think the difference equation is a better formulation of dynamical systems than the differential equation and is more intuitive

[@chadyonfire7878]

Really Nice

[@Nim2]

Thank you for this video. It makes me excited to learn more about my courses I'm currently taking: Differential equations and numerics. Is it possible to do research in e.g. Computational Neuroscience coming from a purely math background?

[@martinsanchez-hw4fi]

Hi! Awesome Video. What do you use for your videos? I really admire the quality

[@ArtemKirsanov]

Thank you! Mostly After Effects + Python (matplotlib for mathematical animations)

[@JorgeHermiloVegaAvalos]

OMG Literally my phd studies are related to this, where was this video 1 year ago when I needed it :((( . Also! Which software are you using for such beautiful animations?? Love the video!

[@syedanabila9546]

Your Fan From Bangladesh 🇧🇩

[@GeoffryGifari]

Ever seen the character "Milo" from the movie "Atlantis: The Lost Empire"?

[@666shemhamforash93]

Love this idea for a series! Do you think you'll work up to population dynamics and RNNs?

[@90800905675]

The part about limit cycles is wrong: the Lotka-Volterra equations (the differential equations you show) do not contain any limit cycle, as a limit cycle must be an isolated closed-loop trajectory, meaning all neighboring trajectories (in an open neighborhood) either spirals in or out, which is not the case here. As all neighboring trajectories are closed-loop trajectories themselves, this indicates that there is not an infinite number of limit cycles as you suggest (there are no limit cycles).

[@vaioslaschos]

And since everything changes all the time, DE are the language of being :-)

[@writerightmathnation9481]

@ 13:00, you incorrectly labeled the derivatives of populations as populations

[@tim40gabby25]

Top notch. Amateur here. Understood.

[@AntonioRonde]

good video

[@GeoffryGifari]

If the output of a *single* neuron depends on its own state some time ago, does that mean a single neuron has its own "memory"? If so, do we know the mechanism behind this memory?

[@Fracasse-0x13]

How does previous state translate to memory?

[@GeoffryGifari]

@@Fracasse-0x13 Imagine if the neuron's output _right now_ depends on its state at an earlier _range_ of time, then there is information stored on what the states are during that range of time so that the neuron can "know" If the neuron's output now only depends on its state _just immediately_ before (infinitesimal slice of time), the concept I mentioned above is unnecessary But if a neuron's output now depends on its state not just immediately before, but also on how its state evolved for the past 100 miliseconds for example, that evolution of states in a finite duration is an information that the neuron "knows" to spit out the right output

[@Fracasse-0x13]

@@GeoffryGifari So I get that the sequence of past interactions can leave behind some state information for a short term duration of time since each interaction changes chemical properties such as ion concentration and changes in the synapse etc. But I don't see why that would be described as the neuron "knowing" how to process the next input or smt?

[@GeoffryGifari]

@@Fracasse-0x13 I phrased it as a neuron "knowing its evolution of state going back a finite span of time", to contrast it with simple mechanical motion, like how position and momentum are described in the video. Example: 1. A particle following newton's laws: the position and momentum x(t +dt), v(t+dt) can be *fully* determined from x(t), v(t), using the equation of motion. 2. A dynamical system having "memory": to make it easier, let's discretize time. If there are two trajectories (following the same dynamical law) of the system state S(t) (represented by a number, could be ion concentration or something) for t=0 to t=5 S(t) = 0.4 -> 1.3 -> 2.7 -> 3.3 -> 3.6 -> S(5) S(t) = 8.4 -> 8.3 -> 8.0 -> 5.9 -> 3.6 -> S(5) The value of S(t) at t=5 for the two trajectories *will not be the same* even though the state just before (S(4)=3.6) are equal. The states going back several units of time matter here. Hence, to get S(5) from S(4), the extra information regarding the past several states needs to be stored somewhere (what I referred to as "knowing"). Can you see the contrast between the two examples?

[@berlinisvictorious]

The thumbnail was enough for me to click

[@RayaneAoussar]

do you use manim for the animation and captions please?

[@ShanDurgut]

How many months of subscriptions so I can appear on your sponsor list page?

[@letsjoinhands]

So a derivative is like a moving gradient measure?

[@GeoffryGifari]

Sounds very physics-y

[@mauroabidalcarrer4083]

awesome

[@kanishktantia7899]

Your videos are very precise and content rich

[@15tatt]

This is absolutely brilliant!!!! Tysm for this!!

[@mike-q2f4f]

Reached my equilibrium point! What?? I'm stuck at ZERO FOREVER?!

[@EstherChira0000]

😂🫡🫂🫀

[@GEMSofGOD_com]

Только filmmaker'у позволительно носить hoodie с пальто

[@tikarambhusal8657]

Love

[@Leo-di9fq]

Thank for uploading. Will watch it soon :)

[@brain_not_braining-0410]

There isn’t such course called vector calculus in brilliant that is accessible to me. Is it my device’s problem? Please help me……

[@Spriglithika]

Artem is the king