I have studied mechanical engineering for almost 5 years now, and this is the best explanation of PDE´s and fourie series I have ever heard. Thank you very much for fantastic illustrations and intuitive explanations.
@Kaynbock Mehr being a high high school student who has only learnt 1st order "simple" differential equations, these series of 3-4 video of differential equation literally took me 4-5 hours to grasp.
Next up, we'll look at how to solve this with Fourier series, including some discussion of boundary conditions. Stay tuned! Edit: I see a number of questions about changes at the boundary, so maybe I’ll add a quick note. For example, some of you ask if a function with constant non-zero slope is stable. Indeed, this is something that needs to be specified for a well-defined solution, so good question! The heat equation as described here only describes the interior. The easiest boundary condition to work with is when each endpoint is held fixed, e.g. if the ends of the rod were somehow constrained not to change temperature. In that case, straight lines are a stable solution. But other conditions can be specified too, as you’ll see!
Thanks for this, writing some coursework on this very topic right now and this really helped clear some stuff up, certainly one of your best series. Also nice choice of numbers @ 3:45
What if the temperature distribution is linear? Then the second partial with respect to x is zero but my gut says that temperature should still ballance out
I used to hate maths in a very profound manner. The reason was that it was presented in a manner like a recipe...do this that and the other in such and such a way and good food comes out. There was no understanding of what was going on and this was most frustrating. The internet, through people like 3 blue 1 brown, helped to propel me to the opposite side of the fence. Although I am no mathematician, I can now appreciate and admire the beauty and power of mathematics. There was clearly a lot of work behind this video to illustrate a complicated subject relatively easily. I wished I had access to such a tool when I was much younger. It would greatly help the younger generation to give them access to material such as this and to encourage them not to shy away from maths. As with most things beautiful, their creation is not easy but nothing to be terrified of either.
This is why a good teacher is so extremely important. Bad teachers present the subject matter, and the students are obligated to practice is, and start to dislike it. Good teachers explain with passion what their subject matter is used for, why it is done this way, and how amazing it is to capture something complex in such a simple way, and the students become intrigued and start to share in the teacher's passion.
AnteConfig Yes it’s from “somewhere”, the land of the 9 year olds. If one these formerly mentioned 9 year olds posts a good meme. The highest level of respect a 9 year old can show another 9 year old is to typ Big pp. One thing that could be off use is to clarify who a 9 year old is. The concept of a 9 year old is bigger then age. You have to be apart of something much more meaningful. You have to be apart of Pewdiepie’s loyal following.
I'm a computer science grad and I've taken a handful of classes which required the use of ODEs and PDEs. After watching this video, I feel like I have finally gained a full conceptual understanding of how they fit into the larger scheme of operations in math and cs. The visualizations you created were absolutely incredible, but the explanation was perfect. Thank you so much!
Likewise...The only classes I used DE’s in really were for Engineering Dynamics and Vibration Analysis (Civil Engineer) but I never really understood what was going on, this is a great video
It's more that the essence of mathematics is not to solve complicated problems, but instead build a landscape of definitions around the problems so that they become simple.
Having a framework which just exists outside of life implies math to be embedded in the foundations of the universe, which isn't the case If that were so, every single mathematical expression would have physical implications Or more explicitly: there are unphysical solutions of General relativity. GR is math. So that math has to come from our minds since it doesn't describe anything in our world.
this series makes me feel like i know more about DEs than i actually do. so i watch this, get confident i can solve some problem on my mind, and then realize that understanding the general mathematical ideas behind the concept does not automatically translate into being able to solve specific problems
3Blue1Brown, this kind of stuff is what I use on a daily basis as a software/mechanical engineer. One of the only disappointing aspects of my work is my inability to describe what I do to the layman. I have to omit huge elegant ideas. I really like that you've captured these ideas in a beautiful and easy to digest way. I cannot wait to see and share the rest of this series.
What do you mean software/mechanical engineer? I'm mechanical and really don't know how I could be both, so I'm very curious as I enjoy some software work and more complicated math.
@@connorskudlarek8598 sorry for the slow reply! I develop internal software tools for an AM startup. We have a welding system with a high dimension parameter space. My team and I do everything from simple GUI design to thermal simulation to g-code. Right now we're testing the waters with ML.
Congrats for not giving up learning this. I just got introduced to this topic last week by my lecturer and almost losing any interest to look it out. Thanks for the inspiration
A constant and e^x are walking down the street. Suddenly the constant screams a horrible sound and yanks e^x in an alley. "There's a differential operator coming against us - we must run or he will reduce me to nothing!" e^x answers calmly "Ok, you run - I'll be fine, the diffop can't hurt me at all". While the constant makes for his escape, e^x keeps walking. When approached by the differential operator - e^x says in a smug voice Hey, how's it hangin'? I'm e^x. The differential operator replies Oh, hi. I'm d/dy.
Just want to thank you for what you do for me and milions of other students, trying to understand such a difficult (but very intuitive after your videos) area of math. Your explanation if very clear, animation is outstanding. I really hope you will continue doing videos this way.
I bet most university teachers don't have a clue of what they are teaching their students. Imagine if math was taught like this in colleges. (chuckles)
@O r a n g You're right. People love 3B1B more than I thought. The only person at my high school I know who knows who 3B1B is. is my math teacher. It's amazing how he can inspire people to love Mathematics. Especially math of Multivariable Calculus.
@@AK-km5tj Yeah, I've done a math phd, a job in math education, and now I'm at a tech company, and regardless of where I am, I find that fairly few people know 3Blue1Brown. So I evangelize a bit. I'm giving a presentation on Friday in which I'll be referencing him.
@@AK-km5tj When I was young I found math difficult and frustrating, but then once I got decent at it, I started to see how beautiful and extraordinarily useful it is. If you can understand this stuff in high school, you have a great start on life. Good luck, and keep learning friend!
Never more clearly explained. Modern students of mathematics are so fortunate. Back in the day (yikes!!), it took me days to understand what has been outlined here in minutes. I second the notion made in the comments to do a video on the graphics tools used. Absolutely stunning.
This is probably one of the most beautiful, satisfying videos I've ever ever seen in my lifetime. I sometimes have the wish of making TH-cam videos on math or physics in my language (br portuguese), but every time I come visit this channel I feel like I'm far from ready. Thank you Sir!
I'm Italian, and I haven't yet formally studied these topics, but your explanatory skills are incredible, you are able to discretize a complex problem in all its basic steps and then put it all back together. I understood practically everything. I don't think I can solve a similar problem by myself, but it's a step forward, really thanks
Mechanical engineering student here! I've had a math professor literally tell my class that he will make us suffer and suffering is necessary to learn. So, thank you for not making me suffer and allowing me enjoy learning about math!! :)
Teachers like that set me back years in learning mathematics, when you preface something as a chore you shouldn't be surprised why students aren't excited about studying the content (unless they are masochists), teachers like Grant are the opposite, his enthusiasm over the years has pushed me to explore and begin to love the math I simply put in the "chore" basket.
I am a student, currently at my second year of my bachelor degree at Physics and Maths. The past semester was more hectic than ever. Especially now while doing the finals of this semester's courses, watching a video like this is so refreshing, and reignites my drive towards what is bound to come along the way. I love talking and listening about Math and Physics, in a figurative and passionate way. I like seeing the beauty of it, that's why I'm doing my degree. Thank you for lightening up my morning!
Y'know, I've been at calculus courses, 1 and 2, at uni. They only taught me how to solve these equations, not what they actually mean intuitively. But I am glad that people like you exist out here, teaching us math the way its meant to be understood. Thank you!
16:26- Indeed a star who has been enlightening millions, like this video that intuitively explained the tough partial derivative easily using his uniquely powerful 3d animation model.
Learning about this isn't exactly in my major of studies but it really is helping me understand many other concepts more intuitively...thanks for the awesome video as always!!!
I like the little easter egg at 3:49 of 7.389 for e², 1.618 as the golden ratio at 3:54 and the controversial pi or the double of 3.14 when you were showing a change in your graph at 4:00
Just WOW... Generally the Fourier equn. is derived by cartesian cube and using taylor series in books and classes..but even after that it is not as satisfying as your explanation of 'comparing it to avg of neighbouring points'... Your way of diving into complexities is very helpful and intuitive and much appreciated. Eagerly waiting for next chapter. 😀😀
Man, the way that a concept so seemingly difficult to comprehend so easily crumbles down to just a matter of simple calculation i cant help but watch with a huge stupid grin on my face.thanks for the experience.
Always he has such a beautiful and intuitive perspective that reduces the complexity of intimidating mathematical objects to something simple and approachable. This is probably how Fourier himself built it up.
As a child I didn't like mathematics. I couldn't grasp the abstract nature of numbers and when I was young nobody taught me about number lines or visual interpretations. In middle school my grades were abysmal and my math teacher at the time told me I should just give up because I don't have the 'head' for it. This wasn't a problem because I never planned a math minded career, but 20 years later I'm back at university studying Computer Science. I've had been having a huge amount of trouble with discrete maths, proofs, calculus, linear algebra and now ODEs/PDEs, until I found 3blue1brown videos. Suddenly, concepts that were foreign and hard to understand I can actually grasp in a visual and intuitive way. I had grown to hate mathematics over my life, but with these videos that hate has turned into love and understanding. I can't thank this channel enough for changing my life in such a profound way.
The effort, intuition and love that goes behind these videos is so real and well thought and the eloquence that comes out is satisfying. It’s about time that education is revamped as rigorously and intuitively as in 3B1B... 💕
I think just about any math class at any level could benefit from 3d animation like this. Maybe it's just my own learning style, but seeing these real-time visuals of how things change and where things go makes a HUGE difference in my understanding.
Did this guy just draw the letter 'f', treble clef, and batman's iconic symbol with variations of rotating vectors? It even projected it in time-domain (looks like it's Gibbs phenomenon) in a smooth and clever animation. This channel is a beast in explaining the most fundamental discoveries in physics. Great, tangible books also offer good pictures of these situations but seeing it in real video/animation is extremely satisfying and enlightening.
I've recognised from these videos that the reason I scraped through math and physics in university is because with so much work to do, and so many problems to learn to solve, not enough time was spent on gaining intuitions. I think if I had learned the intuitions for these concepts I would have fared better. I didn't realise how much intuitions would have helped. Maybe I could have spent more time on investigating the intuitions if I knew. University was around 10 years ago. I didn't think I'd ever be looking at these kinds of topics ever again. The way 3blue1brown explains these things and provides the intuition has drastically changed and improved my understanding of these concepts. I have a new appreciation for Fourier transforms and waves(from another 3b1b series), and differential equations now. Topicst that I hated back then, I am watching and learning from these videos now with a lot of fascination and interest.
The animations are beyond phenomenal, so original and so effective in putting the ideas across. Can't appreciate him enough for putting together all these lessons.
Man....I feel so lucky to have found this amazing channel for learning. I want to thank and give my gratitude to the person/s behind all this hard work.
This video was just downright awesome! I used to be intimidated by partial derivatives, but the graphs and animations helped me understand that they are quite simple. Great job 3b1b.
All these series are beyond phenomenal! To say they are ultra-meticulously designed and edited- would not do the justice. This is a masterpiece! Hats off!
I have a degree in structural engineering and have spent my time in college with ODE and PDE. This is by far, the most elegant and intuitive description of PDE than any of my brilliant professors were able to give us. Your channel is brilliant.
I have being studying numerical methods to solve PDEs for the last 4 years at university. I was feeling pretty confident on the topic. Now you come around and turn my world upside down - each one of your videos gives me a new, powerful way of looking at the same old problems! Truly eye-opening. Case and point: your explanation of the second derivative as moving towards the average of its neighbors is nothing other than a central difference scheme. I've been using it for years and you just gave me a totally new insight into how it works. Just... Wow. PS: your visualisations are freaking amazing as well. I wish professors used such good material as well. If I'm ever teaching any of these topics, I'll be sure to make watching your videos compulsory ;)
can't even find the words for how good you can make people understand such hard things ! as a student in theoretical mechanical engineering, I'm just amazed and so thankful that u gave some color and visuals to the letters and white boards of my teachers at university ! thanks ! aaaaaa LOOOOOOOTTTTT
How? How how how does this guy have the best graphics? I’ve never been able to get over how well he explains everything visually. Honestly the best on TH-cam. Thank you for helping me both feel dumb AND smart ish at the same time!
The graphs and animations are just F** mind blowing... I hope not to sound too freak when I say that this kind of video profoundly relax me into a chill-active mental state
This, and the previous video, cracked open so many relationships between how ancients saw planets - "wanderers" - to how Illustrator's path handles pull curves along, to Fourier transforms, that I'm tempted to find the second derivative to how quickly my mind has been blown tonight.
Simply amazing! Boiling the whole heat equation down to 3 points that essentially explains the PDE intuitively. Fabulous job. Please keep creating such content explaining the essence of math through beautiful visualizations.
100 years from now, people will watch this video and be thankful that you made it. It's among the very best of what human beings and do with the internet and personal computer technology. Thank you.
If ANYONE had explained the Laplacian as the relationship of the value of a point to the average value of its neighbors to me during my fluids class, my grade could have been a full letter higher.
whosoever you are....you are a genius....its been 5 years since i have studied the PDEs for the first time and today i have understood them. The fact that no teacher could ever tell me the statement 'rate of change of rate of change' tells us how messed up our education system is....this channel should be made compulsory for first year engineering undergrads
This one i have to give is the best among all of your videos Up to the point, no wierd references, understandable, no need to listen carefully yet you understand, Animation god, best in all🎉❤
I am doing PhD in Hydrology and this is the best illustration I have seen till date. You have got to appreciate the amount of effort this man put into this.
I really enjoy this video! One of my favorites from you so far, you really drive the point home. I especially like how far you've come with animating 3-dimensional graphs. :D
Learning deeper and more exquisite maths later in life adds a layer of appreciation to the experience of seeing the world in such new ways.For me there are times when I can literally compare the process to meditation.Working through a problem quiets the mind and heightens the mood in a real and meaningful way.Out of nowhere the mind seems stretched in all respects.
I wonder what to address you as - a teacher, a mathematician, an artist or more precisely all of them? Souls of Sir Issac Newton and many more must be very proud of you mate!
Im rewatching this for the 3rd time with a genuine wish to understand PDEs while they have nothing to do with my line of work nor do I need them for school n such You give off the same energy as Stanford's Dr Sapolsky, in the sense that you beam knowledge into our heads.
My teacher told us the procedures of solving maths that are going to appear in our exam and all the time l was thinking ' WHAT the hell is this PDE" but thanks to you l have got the visualization of what exactly PDE is and how it's a world changer.
For those who are venturing in to world of solving PDEs.. as Grant nicely puts it from 3:04 to 3:11.. this approximation is the heart of solving for pdes...
A modern mental masterpiece.
Yepp it is truly beautiful! Also, it is a delight to see you here sir! Please keep up the good work😄💎
why only 3 replies?
@@VinOnline now 3
4
5
I can not give enough praise on the quality of animation coupled with the explanation. Amazing - Thank you
Same here.
yes, its amazing!
I want my student loans back, amazing!!! I spent hours and loans trying to figure it out. Thank you thank you
Totally agreed, it's phenomenal.
Ditto.
3:45 i love how x goes from pi to e^2 to phi. Amazing little easter egg.
Edit: what the heck likes
and then to tau
I saw it too.
You guys definitely got some sharp observation skills.Thanks for mentioning!
Yeah, nice one, guys!
The Easter egg at Easter Sunday
3B1B deserves a Nobel Prize for explaining math! Simply outstanding, yet again.
Pero vaya!!!
It is the Fields Medal i think...
@@divyansharora6788 In field of math education, it is Leelavati Award
AGREED 100 PERCENT, but I think it is is called the field's medal 😂
A Nobel Peace Price
I have studied mechanical engineering for almost 5 years now, and this is the best explanation of PDE´s and fourie series I have ever heard. Thank you very much for fantastic illustrations and intuitive explanations.
Malthe Wellendorf Gissel i studied electrical and we also need to be comprehensive in PDE
I'm in research physics, and this is a helpful starter
P
1 year after my msme lol
@Kaynbock Mehr being a high high school student who has only learnt 1st order "simple" differential equations, these series of 3-4 video of differential equation literally took me 4-5 hours to grasp.
Those graphics are really getting exceptionally good! The 2d representation animation at 4:13, for example, is just gorgeous.
Yeah that moment struck me too. He's getting quite good.
I love the Fourier series section.
I came to say the same thing. I hope it does not take a lot of time to generate them as it looks so
does anyone know what tools he uses?
He makes his own tool in Python, you can download it here github.com/3b1b/manim
Next up, we'll look at how to solve this with Fourier series, including some discussion of boundary conditions. Stay tuned!
Edit: I see a number of questions about changes at the boundary, so maybe I’ll add a quick note. For example, some of you ask if a function with constant non-zero slope is stable. Indeed, this is something that needs to be specified for a well-defined solution, so good question! The heat equation as described here only describes the interior. The easiest boundary condition to work with is when each endpoint is held fixed, e.g. if the ends of the rod were somehow constrained not to change temperature. In that case, straight lines are a stable solution. But other conditions can be specified too, as you’ll see!
Cant wait to see if you use the only good convention for the prefactor
Thanks for this, writing some coursework on this very topic right now and this really helped clear some stuff up, certainly one of your best series. Also nice choice of numbers @ 3:45
What if the temperature distribution is linear? Then the second partial with respect to x is zero but my gut says that temperature should still ballance out
@@joshuagross6022 There was no assumption about the boundary in this vid, so it would correspond to a constant heat flow
@@aksel9290 1) pi 3) Golden ratio 4) tau
What's 7.380?
Edit: Sorry, 7.389
Edit: Nvm, I read it in comments. It means e^2.
I used to hate maths in a very profound manner. The reason was that it was presented in a manner like a recipe...do this that and the other in such and such a way and good food comes out. There was no understanding of what was going on and this was most frustrating. The internet, through people like 3 blue 1 brown, helped to propel me to the opposite side of the fence. Although I am no mathematician, I can now appreciate and admire the beauty and power of mathematics. There was clearly a lot of work behind this video to illustrate a complicated subject relatively easily. I wished I had access to such a tool when I was much younger.
It would greatly help the younger generation to give them access to material such as this and to encourage them not to shy away from maths. As with most things beautiful, their creation is not easy but nothing to be terrified of either.
same here
I feel you on that!
preach it bro..
I definitely agree
This is why a good teacher is so extremely important. Bad teachers present the subject matter, and the students are obligated to practice is, and start to dislike it. Good teachers explain with passion what their subject matter is used for, why it is done this way, and how amazing it is to capture something complex in such a simple way, and the students become intrigued and start to share in the teacher's passion.
I've watched countless 3B1B videos and they're all illuminating and high-quality. This one, among those, is an absolute masterpiece.
2:23
Mathematicians: function
Linguists: letter
Musicians: forte
Gamers: respect
Hotel: Trivago
@@subhramitbasu3886 hotel: Frivago
Big pp
@@arvidjohansson3120 I'm so confused... is this from somewhere?
AnteConfig Yes it’s from “somewhere”, the land of the 9 year olds.
If one these formerly mentioned 9 year olds posts a good meme. The highest level of respect a 9 year old can show another 9 year old is to typ Big pp. One thing that could be off use is to clarify who a 9 year old is. The concept of a 9 year old is bigger then age. You have to be apart of something much more meaningful. You have to be apart of Pewdiepie’s loyal following.
This channel made me realized that I don't actually hate math.
Same...
@Leopold Maximilian von Hagen Believe me, you can't hate math when you're self-learning.
Except if you hate yourself, of course.
@wickedcat We are far from being that rational, my fellow human.
@@segmentsAndCurves we are rational but not in the philosophic way. In the mathematic way we are pretty much rational
@@fabio19h You got me good. NOW GET OUT OF HERE.
I’ve done the multivariable calculus lessons you recorded on Khan Academy and I gotta say, I’m getting flashbacks
I've just had an orgasm...
Me too!
Good ones, I hope?!
Confused Dave Of course mate
Can you put the link of these lessons to all of us?
I'm a computer science grad and I've taken a handful of classes which required the use of ODEs and PDEs. After watching this video, I feel like I have finally gained a full conceptual understanding of how they fit into the larger scheme of operations in math and cs. The visualizations you created were absolutely incredible, but the explanation was perfect. Thank you so much!
can you reference some pdfs or channels to learn odes and pdes related to computer science?
Yeah @anti gy I have the same question, any recommendations @Kraylus?
tf2 engineer tf2 engineer
comment exeptional n a created have you
Likewise...The only classes I used DE’s in really were for Engineering Dynamics and Vibration Analysis (Civil Engineer) but I never really understood what was going on, this is a great video
Omg !, he should be given the highest award in today's world for explaining partial differential equations.
Respect and a salute
5:30-6:15 Got it! Partial differential equations aren't actually partial. They are complete - but only as a description of part of the system. Thanks!
I wasn't understanding a thing until I read this comment...
Thanks 👍
Oscars award for animation to be given to this channel
move over Spiderverse
Nothing more wholesome and satisfying than a 3Blue1Brown video
If i could like your comment 100000000 times......
A video from eugene khutoryansky is also a dream
*The essence of mathematics is not to make simple things complicated, but to make complicated things simple* 🕊️
3rd semester mathematics students would like to know your location
Me too
It's more that the essence of mathematics is not to solve complicated problems, but instead build a landscape of definitions around the problems so that they become simple.
@@timh.6872 Yeah! The question is.. Is math a language created by us humans to understand the world OR is math a universal language? 📚
Having a framework which just exists outside of life implies math to be embedded in the foundations of the universe, which isn't the case
If that were so, every single mathematical expression would have physical implications
Or more explicitly: there are unphysical solutions of General relativity. GR is math. So that math has to come from our minds since it doesn't describe anything in our world.
I'm a postgrad and your videos have saved me more than once. Thank you and please continue to remind people of how beautiful math is
this series makes me feel like i know more about DEs than i actually do. so i watch this, get confident i can solve some problem on my mind, and then realize that understanding the general mathematical ideas behind the concept does not automatically translate into being able to solve specific problems
3Blue1Brown, this kind of stuff is what I use on a daily basis as a software/mechanical engineer. One of the only disappointing aspects of my work is my inability to describe what I do to the layman. I have to omit huge elegant ideas. I really like that you've captured these ideas in a beautiful and easy to digest way. I cannot wait to see and share the rest of this series.
I'm a quantum physicist faced with the same difficulty; this channel is a great resource.
What do you mean software/mechanical engineer? I'm mechanical and really don't know how I could be both, so I'm very curious as I enjoy some software work and more complicated math.
Mecatronics?
@@connorskudlarek8598 sorry for the slow reply! I develop internal software tools for an AM startup. We have a welding system with a high dimension parameter space. My team and I do everything from simple GUI design to thermal simulation to g-code. Right now we're testing the waters with ML.
Kindly explain the pi shifted heat transfer as isothermal expansion.
This is so great, I finally understand this concept after 32 years
wait what
Wait what 2 !
Congrats for not giving up learning this. I just got introduced to this topic last week by my lecturer and almost losing any interest to look it out. Thanks for the inspiration
Dont need to be ashamed. Most textbooks are not really made to understood, they are just products to remember.
@@howmathematicianscreatemat9226 that seems to be the case
Thank god for TH-cam
A constant and e^x are walking down the street. Suddenly the constant screams a horrible sound and yanks e^x in an alley.
"There's a differential operator coming against us - we must run or he will reduce me to nothing!"
e^x answers calmly "Ok, you run - I'll be fine, the diffop can't hurt me at all".
While the constant makes for his escape, e^x keeps walking. When approached by the differential operator - e^x says in a smug voice
Hey, how's it hangin'? I'm e^x.
The differential operator replies
Oh, hi. I'm d/dy.
haha
This is Mathematics, art, science, poetry in one package..Mindblowing and subtle at the same time
Great observation
Just want to thank you for what you do for me and milions of other students, trying to understand such a difficult (but very intuitive after your videos) area of math. Your explanation if very clear, animation is outstanding. I really hope you will continue doing videos this way.
seconded
At last -- a channel that actually shows the guts of the math that everyone else glosses over. Yah. I'm hooked.
Well, there are a lot more guts he's not showing, but he does better than pretty much every youtuber that's not just a professor giving a lecture.
I bet most university teachers don't have a clue of what they are teaching their students. Imagine if math was taught like this in colleges. (chuckles)
These animations are mindblowing, so much easier to visualize like this
pleasantly surprised to see 3k views in 10 minutes on a math video
@O r a n g Now 25k
@O r a n g You're right. People love 3B1B more than I thought. The only person at my high school I know who knows who 3B1B is. is my math teacher. It's amazing how he can inspire people to love Mathematics. Especially math of Multivariable Calculus.
I love this channel! ❤️
@@AK-km5tj Yeah, I've done a math phd, a job in math education, and now I'm at a tech company, and regardless of where I am, I find that fairly few people know 3Blue1Brown. So I evangelize a bit. I'm giving a presentation on Friday in which I'll be referencing him.
@@AK-km5tj When I was young I found math difficult and frustrating, but then once I got decent at it, I started to see how beautiful and extraordinarily useful it is. If you can understand this stuff in high school, you have a great start on life. Good luck, and keep learning friend!
And, I just actually think that this is the best channel to gain rock solid intuition in math. Thank you ☺️
At 3:35 I have a feeling, that the script goes: "...what the f. is going on in here" and you somehow saved the situation at the very right moment
Me: "I'll just watch the first 5 minutes to see what it's about and get back to work"
*watches the whole 17 minutes*
Never more clearly explained. Modern students of mathematics are so fortunate. Back in the day (yikes!!), it took me days to understand what has been outlined here in minutes. I second the notion made in the comments to do a video on the graphics tools used. Absolutely stunning.
This is probably one of the most beautiful, satisfying videos I've ever ever seen in my lifetime. I sometimes have the wish of making TH-cam videos on math or physics in my language (br portuguese), but every time I come visit this channel I feel like I'm far from ready. Thank you Sir!
I'm Italian, and I haven't yet formally studied these topics, but your explanatory skills are incredible, you are able to discretize a complex problem in all its basic steps and then put it all back together. I understood practically everything. I don't think I can solve a similar problem by myself, but it's a step forward, really thanks
16:10 infinite powers Steven Strogatz
the reason why i love this channel is it can always give a “wow moment” of thinking about something in a different way
Mechanical engineering student here! I've had a math professor literally tell my class that he will make us suffer and suffering is necessary to learn. So, thank you for not making me suffer and allowing me enjoy learning about math!! :)
Teachers like that set me back years in learning mathematics, when you preface something as a chore you shouldn't be surprised why students aren't excited about studying the content (unless they are masochists), teachers like Grant are the opposite, his enthusiasm over the years has pushed me to explore and begin to love the math I simply put in the "chore" basket.
nice profile picture
I am a student, currently at my second year of my bachelor degree at Physics and Maths. The past semester was more hectic than ever. Especially now while doing the finals of this semester's courses, watching a video like this is so refreshing, and reignites my drive towards what is bound to come along the way. I love talking and listening about Math and Physics, in a figurative and passionate way. I like seeing the beauty of it, that's why I'm doing my degree.
Thank you for lightening up my morning!
Y'know, I've been at calculus courses, 1 and 2, at uni. They only taught me how to solve these equations, not what they actually mean intuitively. But I am glad that people like you exist out here, teaching us math the way its meant to be understood. Thank you!
16:26- Indeed a star who has been enlightening millions, like this video that intuitively explained the tough partial derivative easily using his uniquely powerful 3d animation model.
Learning about this isn't exactly in my major of studies but it really is helping me understand many other concepts more intuitively...thanks for the awesome video as always!!!
I like the little easter egg at 3:49 of 7.389 for e², 1.618 as the golden ratio at 3:54 and the controversial pi or the double of 3.14 when you were showing a change in your graph at 4:00
Just WOW... Generally the Fourier equn. is derived by cartesian cube and using taylor series in books and classes..but even after that it is not as satisfying as your explanation of 'comparing it to avg of neighbouring points'... Your way of diving into complexities is very helpful and intuitive and much appreciated. Eagerly waiting for next chapter. 😀😀
Man, the way that a concept so seemingly difficult to comprehend so easily crumbles down to just a matter of simple calculation i cant help but watch with a huge stupid grin on my face.thanks for the experience.
Always he has such a beautiful and intuitive perspective that reduces the complexity of intimidating mathematical objects to something simple and approachable. This is probably how Fourier himself built it up.
You are really passionate with mathematical concepts , keep on going like this you are helping many of us with your great efforts :).
The 3D Animation on this is amazing.
3:45 x goes from π (approximately 3.142) to e^2 (approximately 7.389) and then to the golden ratio (approximately 1.618)
What a nice detail!
Shocked that it didn't start at the true circle constant, tau.
Unacceptable.
As a child I didn't like mathematics. I couldn't grasp the abstract nature of numbers and when I was young nobody taught me about number lines or visual interpretations. In middle school my grades were abysmal and my math teacher at the time told me I should just give up because I don't have the 'head' for it. This wasn't a problem because I never planned a math minded career, but 20 years later I'm back at university studying Computer Science. I've had been having a huge amount of trouble with discrete maths, proofs, calculus, linear algebra and now ODEs/PDEs, until I found 3blue1brown videos. Suddenly, concepts that were foreign and hard to understand I can actually grasp in a visual and intuitive way. I had grown to hate mathematics over my life, but with these videos that hate has turned into love and understanding. I can't thank this channel enough for changing my life in such a profound way.
WOW, I could never understand what my PDE lecturer tried to explain without you! :) Thanks!
The effort, intuition and love that goes behind these videos is so real and well thought and the eloquence that comes out is satisfying. It’s about time that education is revamped as rigorously and intuitively as in 3B1B... 💕
I felt this one is more intuitive than the first one. Animation just blew my mind.
I think just about any math class at any level could benefit from 3d animation like this. Maybe it's just my own learning style, but seeing these real-time visuals of how things change and where things go makes a HUGE difference in my understanding.
Did this guy just draw the letter 'f', treble clef, and batman's iconic symbol with variations of rotating vectors? It even projected it in time-domain (looks like it's Gibbs phenomenon) in a smooth and clever animation. This channel is a beast in explaining the most fundamental discoveries in physics. Great, tangible books also offer good pictures of these situations but seeing it in real video/animation is extremely satisfying and enlightening.
I've recognised from these videos that the reason I scraped through math and physics in university is because with so much work to do, and so many problems to learn to solve, not enough time was spent on gaining intuitions. I think if I had learned the intuitions for these concepts I would have fared better. I didn't realise how much intuitions would have helped. Maybe I could have spent more time on investigating the intuitions if I knew.
University was around 10 years ago. I didn't think I'd ever be looking at these kinds of topics ever again. The way 3blue1brown explains these things and provides the intuition has drastically changed and improved my understanding of these concepts. I have a new appreciation for Fourier transforms and waves(from another 3b1b series), and differential equations now. Topicst that I hated back then, I am watching and learning from these videos now with a lot of fascination and interest.
The animations are beyond phenomenal, so original and so effective in putting the ideas across. Can't appreciate him enough for putting together all these lessons.
Man....I feel so lucky to have found this amazing channel for learning. I want to thank and give my gratitude to the person/s behind all this hard work.
This video was just downright awesome! I used to be intimidated by partial derivatives, but the graphs and animations helped me understand that they are quite simple. Great job 3b1b.
All these series are beyond phenomenal! To say they are ultra-meticulously designed and edited- would not do the justice.
This is a masterpiece! Hats off!
I have a degree in structural engineering and have spent my time in college with ODE and PDE. This is by far, the most elegant and intuitive description of PDE than any of my brilliant professors were able to give us. Your channel is brilliant.
I'm more excited about watching the next episodes than any other tv show
I like how at 3:46, the notch goes from π to e^2 to ϕ to τ. Nice touch, and great video as always!
I have being studying numerical methods to solve PDEs for the last 4 years at university. I was feeling pretty confident on the topic. Now you come around and turn my world upside down - each one of your videos gives me a new, powerful way of looking at the same old problems! Truly eye-opening.
Case and point: your explanation of the second derivative as moving towards the average of its neighbors is nothing other than a central difference scheme. I've been using it for years and you just gave me a totally new insight into how it works.
Just... Wow.
PS: your visualisations are freaking amazing as well. I wish professors used such good material as well. If I'm ever teaching any of these topics, I'll be sure to make watching your videos compulsory ;)
can't even find the words for how good you can make people understand such hard things ! as a student in theoretical mechanical engineering, I'm just amazed and so thankful that u gave some color and visuals to the letters and white boards of my teachers at university ! thanks ! aaaaaa LOOOOOOOTTTTT
How? How how how does this guy have the best graphics? I’ve never been able to get over how well he explains everything visually. Honestly the best on TH-cam. Thank you for helping me both feel dumb AND smart ish at the same time!
Man I love how much effort you are putting into this.
THIS IS HONESTLY BEAUTIFUL!
And your teaching skills just keep blowing my mind!!
7:05 is where the awesomeness starts... The way to actually understand equations...
The graphs and animations are just F** mind blowing... I hope not to sound too freak when I say that this kind of video profoundly relax me into a chill-active mental state
This, and the previous video, cracked open so many relationships between how ancients saw planets - "wanderers" - to how Illustrator's path handles pull curves along, to Fourier transforms, that I'm tempted to find the second derivative to how quickly my mind has been blown tonight.
Simply amazing! Boiling the whole heat equation down to 3 points that essentially explains the PDE intuitively. Fabulous job. Please keep creating such content explaining the essence of math through beautiful visualizations.
Never thought I could "come up with" the heat equation, until you said so.
The visualizations, together with the explanations, are absolutely amazing!
This dude is really good at making me believe I understand everything in the moment but afterwards have no clue what I just watched
100 years from now, people will watch this video and be thankful that you made it. It's among the very best of what human beings and do with the internet and personal computer technology. Thank you.
3:37 : What the F...unction
but seriously, thanks for this amazing work!
Haha I also observed it🤣🤣
"Second derivatives gives a measure of how a value compares to the average of it's neighbor." I've never seen second derivative like this.
If ANYONE had explained the Laplacian as the relationship of the value of a point to the average value of its neighbors to me during my fluids class, my grade could have been a full letter higher.
I've just learned this concept today!!! 😭
whosoever you are....you are a genius....its been 5 years since i have studied the PDEs for the first time and today i have understood them. The fact that no teacher could ever tell me the statement 'rate of change of rate of change' tells us how messed up our education system is....this channel should be made compulsory for first year engineering undergrads
Seriously... 3B1B's animations always BLOWS MY FRICKING MIIIND HOOOLY SHIIIIT
Such beautiful representation of abstract ideas.
Loved it.
Teaching the courses that really give people headaches, making them easier to understand. Thank you 3Blue1Brown
Not all heroes wear capes.
Although, I'd like to say... he's not a hero...
He's a legend!
Never tapped faster on a notification
Same here bro😀
Same here. I need to watch it.
I was the 10th one to see it damn
Isn't that always what happens with 3blue1brown videos? :D
Right before finals
This one i have to give is the best among all of your videos
Up to the point, no wierd references, understandable, no need to listen carefully yet you understand, Animation god, best in all🎉❤
I am doing PhD in Hydrology and this is the best illustration I have seen till date. You have got to appreciate the amount of effort this man put into this.
I hope one day you'll explain how the Laplace Transform works :)
He will, check his previous video about ordinary differential equations in the series of images I think it should be the after the next video
Yessssssss. That would be awesome for engineers!
He actually will later in the series! I'm just as excited for it as you are!
and then Mellin transform
I really enjoy this video! One of my favorites from you so far, you really drive the point home. I especially like how far you've come with animating 3-dimensional graphs. :D
Holy cow, that was good! I would place this video immediately below that green citrus video: "sublime"
Learning deeper and more exquisite maths later in life adds a layer of appreciation to the experience of seeing the world in such new ways.For me there are times when I can literally compare the process to meditation.Working through a problem quiets the mind and heightens the mood in a real and meaningful way.Out of nowhere the mind seems stretched in all respects.
I wonder what to address you as - a teacher, a mathematician, an artist or more precisely all of them? Souls of Sir Issac Newton and many more must be very proud of you mate!
This problem is almost identical to my final project in my advanced mathematical methods class for engineers due next week.
Yay matlab.
I'm amazed for the amount of dedication I find on these videos! Keep going!
You are a awesome teacher bro 😁
I always wanted this intuition of calculus which you give on your channel , thanks for your work😀😊
Im rewatching this for the 3rd time with a genuine wish to understand PDEs while they have nothing to do with my line of work nor do I need them for school n such
You give off the same energy as Stanford's Dr Sapolsky, in the sense that you beam knowledge into our heads.
My teacher told us the procedures of solving maths that are going to appear in our exam and all the time l was thinking ' WHAT the hell is this PDE" but thanks to you l have got the visualization of what exactly PDE is and how it's a world changer.
Yay! 3blue1brown uploaded, and another of my favorite youtubers uploaded today too!
If only three more 3b1b channels I would have more frequent notifications.
wish i could thumbs up twice.
this video lads perfectly at the near end of my course in ODEs. Thanks for the intuitive look ahead!
For those who are venturing in to world of solving PDEs..
as Grant nicely puts it from 3:04 to 3:11..
this approximation is the heart of solving for pdes...
Omg! Why I doesnt see this video 20 years ago during my study? Its easy to understand. Step by step. Great, Thank you!