After listening to a lot of teachers, I have to say that you are simply the best explainer I know. Probably one of the greatest teachers of all time. By explaining complex and powerful ideas in such a beautiful and simple way, your work will surely have a big impact on the life of future scientists and engineers. Keep it going man, you are doing an amazing job!
He truly is very good at what he does! You can tell that he has a good understanding of when his explanations are good, and you can tell he takes a lot of time to get to that point.
Grant, you have the unique trifecta: 1. Intelligence to understand these complex topics. 2. Ability (and willingness!) to explain them clearly. 3. Technical chops to animate and edit your explanations. Nothing you do is easy but it is all appreciated by a wide audience.
That is not a unique trifecta by any stretch of imagination. Many have it, and more to the point everyone can. *You* can have that trifecta. If you don't, that's your own choice.
There's also a strong instinct for visual beauty, a tendency toward warm communication, and memory/empathy for what it's like to not know the concepts yet, which are what make 3b1b really stand out, IMO
As I begin my journey to get a physics degree, I can't help but look back and thank you for all the content you've made. Truly inspiring and educational stuff :)
@@spongbong0 im innately a curious person, so physics is a pathway for me to understand how things work. Im particularly interested in how things work on a fundamental level and look forward to learning about relativity and QM in depth. For me, choosing physics is like following a passion; for you, i dont know what physics might be, so take some classes and find out!?
@@lol12313 I want to be an astrophysist please give me some tips on how to get good at physics I practice questions daily but I don't know what else to do
*_Grant, you are the beacon of light in the Math world to me and maybe millions of people around the world._* You have: ✎Talent to understand the complex principles ✎Passion to share your knowledge and love for math to people ✎Acute competency to explain and animate the concepts into common languages for anyone ✎Persistency and hard work that only few people can sustain 🏆🏆Thank you and thank you!!! ================================= Also want to give thanks to the founders of UA-cam!
I’m in the process of writing my thesis for a PhD in theoretical physics and I’ll be completely honest, I cried at how elegant this explanation is. Thank you for helping someone who feels they’ve lost a lot of passion for maths and physics after years of hard work, realise that they still have the capacity to really care about these subjects. Truly thank you.
What made you lose passion along the way? I just finished my thesis for a PhD in math and I'm still excited about the math itself. Worst parts of academia are still stuff outside the math (grant writing, etc..)
Amir, I'm about your age and just finishing a bachelor's degree... If I can, you can... And one of my favorite math teachers is also named A. Ghoreishi. :)
@@skydragon3857 Look for a local college/university, visit their web-site and find the apply button... Also, look for non-traditional student services for help, advice and support.
Somehow this wound up in my recommended, and I’ll be frank here. I’m in 10th grade and am nowhere NEAR the level of algebra and calculus comprehension required for this, but you explained this complex subject so well and fluently and thoroughly that even I managed to roughly understand some of the concepts! Excellent work, and keep it up!
I (a Junior Electrical Engineering Student) went through the same experience time and time again. But, remembering these after a time of learning is a great way to see how far you have come with understanding and knowledge; I did that as I was watching this because I’m going over Fourier Series right now in my Signals and Linear systems class, and I said to myself “wow, I’ve learned a lot, I actually understand where these are coming from!” when I watched this last year, I had no idea where things were coming from, but after learning about the fundamental concepts and applying them, the fog cleared and I actually recognized things. All of this to say, always go back to videos like this to see what you recognize to see what you now know - it’s the joy of learning.
@@foxphire0093 but when I draw I'm not thinking of a formula. The creativity is not pre formulated outside of how the parts relating to the whole. Form AND function.
This video came out while I was taking my intro diff EQ class. Didn't see it till now at 3am. Would have been helpful at the time since my Prof gave zero context for how these equations work and how they can be applied.
This is pure gold for an engineering student like myself. I hope you one day get the recognition you truly deserve for illustrating the ideas this beautifully and clean. Thank you.
same for me... as an engineering student, i've never fully understood the math behind Fourier, limiting myself to apply it mechanically. I know what an FFT and the Fourier series are built for and their importance in signal processing, but the math behind them remains for me some sort of magic even after Math III exam. This, damn this is totally mind blowing.
I am a Math Ph.D holder who's been both teaching and researching the Fourier related field and, HOLY CRAP this is one of the best visual explanation I've seen. I will definitely distribute a reference to this channel wherever I will go.
Doing something like this with video editing software is almost impossible. Each of his videos is entirely produced by a Python program that uses a library he wrote (which is also open source IIRC). I guess that is the only sane way to create videos like this.
After watching this for the 1000th time, I finally had the key intuition necessary to code my own Fourier Transform. As a musician, nothing makes me happier than having my own little Fourier transform now. I just want to thank you for these videos, they’ve completely resparked my joy for math.
@@dracovet777 Sort of lol. Melodyne is way more intense than my algorithm. Since I wrote this I've managed to optimize it using some linear algebra I just learned, but it's still just a basic fourier transform and not anywhere close to an fft
@@sidewinded1 ok so I use python’s numpy library. Long story short I take the inner product of 2 vectors which are representative of the functions you get in the Fourier series. The fancy stuff is making it all compact so I can use it wherever I need to, I basically made that all into a lambda function. I know this isn’t the worlds best explanation but all I’m trying to say is it boils down to how much linear algebra you know.
It's amazing to see all these concepts described with animated drawings. I find it even more amazing that generations of people were able to learn and apply the concepts well before the advent of moving pictures. To really internalize these ideas and visualize these things in your mind must be an amazing experience.
I'm a seismologist and even I don't understand Fourier theory at this level of ease and intuition. You took one of the most complicated concepts in science and made it so beautiful and intuitive.
In all my years at college, I've never seen such a stunning presentation about Fourier series. I can't help but say thank you . This is in a total different level of explanation...
I've never known what even is a "differential equation", and I'm definitely never studying this kind of advanced maths in college. However, this is one of the best youtube series I've ever seen, and this super well-articulated, extremely elegant video has prompted me to express my utmost appreciation for your content, Mr. Sanderson. Truly the best Maths channel in the world.
I took courses on signal & system and digital signal processing before UA-cam was founded. I wish I was born later so I could take advantage of the best explainers like you and the best of visual presentations like this. The timings of items you throw on the screen, the sequence, the connections, and the visual ques you use is beyond precision, beyond exact. This is a God-mode representation of Fourier series in terms of rotating circles! Take a bow!
I’m in Signals right now and watching this definitely helps my overall understanding of why things happen as opposed to just accepting it and moving on
I am an electronic engineer. I took a dozen of courses about Fourier series and transform. I work with spectral analysis on daily basis and this video blew my mind
I've finished a 5-year degree of applied physics, but I gotta say that I never quite fully understood why the Fourier series works. A big reason for that is that there's so many things to learn that you mostly learn the 'how' instead of the 'why'. It makes for quick gains of knowledge, but it simultaneously makes for quick losses of knowledge, as it really is the 'why' that makes for the building blocks of knowledge in the long run. Your channel, and especially this video, masterfully compresses the 'why' into its central components and makes for quick and stable gains of knowledge. In the long run, you will have helped creating a much more efficient, robust and accessible education for everyone. Great job, and keep going!
conacal rubdur it’s a very broad engineering degree (I should probably have written Engineering physics, as that’s its real name), so you can get into most engineering things (except for chemistry, I guess) if you choose the right specialization (i.e. Master’s degree). I myself am working with software development and machine learning!
conacal rubdur Yes, it is computer science! I’d say that more and more engineers go into this field nowadays, despite coming from quite different backgrounds in their bachelor’s. As you might realize, my Engineering physics degree was quite different from what I’m working with now. Basically, my first 3 years (i.e. bachelor’s) consisted of lots of heavy maths and physics, which has given me a solid mathematical foundation to understand most research papers I read on AI and other subjects. In your case, I’d say that most engineering degrees give a good mathematical foundation, though (except maybe for chemical engineering; I don’t know how complicated maths needs to be there), so it’s probably more important to choose a bachelor’s that you could feel motivated for, rather than choosing something that could boost your career. Anyways, owing to your list of subjects, I’d say that mechanical or aerospace engineering would probably be the best bet! I think bachelor’s = undergrad, so you have to decide on your bachelor’s before you get into college. Don’t worry though; the math you learn in one field is often used in the next (such as fourier series), so choosing one specialization doesn’t mean you can’t change your mind in the future! :)
conacal rubdur Yeah, I’d go for mechanical engineering in that case, since it’s broader and, who knows, maybe you’ll find something else that’s more interesting there, and then it’s nice to know that your broad education gives you better opportunities to specialize in that if you want! I have no idea what the chances of landing the jobs you’re listing are, and I’d definitely say that it depends on where you are. Engineers are pretty popular on the job market though, so finding a job shouldn’t be that hard. Regarding the major, I’d say that it also depends on where you are. I’ve heard that in U.S. it’s pretty common to do a bachelor’s work for a while, and then get back to a master’s. Many here hope that the company offers a paid master’s, since doing it on your own very likely costs more than you get back from a future career. In Europe, however, the situation is very different, as we don’t have to pay for each semester. Therefore, we often do a bachelor’s and master’s consecutively, without a break, in order to actually finish our degree. I myself would reason that if I started working after my bachelor’s, I wouldn’t wanna go back to school once I’ve settled into this new lifestyle of getting paid and not having a constant feeling that I have to study. People are of course different, but if you’re in Europe, I’d recommend bachelor’s + master’s in one go, since you then finish everything in one go, and it feels like you continuously improve your lifestyle!
conacal rubdur well, location matters in the sense that your society works differently than in Europe. For you, it costs a whole lot more for each additional semester you study; whilst in Europe, you don’t have that much to lose to study a couple more years. Regarding your question about applying for jobs all over US, I don’t know what’s best, since I don’t live there and don’t know anything about the costs of travelling or how valuable it is to move for jobs there. If it had been me, though, I would have started out looking for jobs nearby, since it’s simpler!
conacal rubdur Yes, that sounds good! Those unemployment rates are very low, so you shouldn’t worry about that. Additionally, if I were to worry about unemployment after graduation, I would take into consideration how easy my job is to automate, since that is a trend that will accelerate. For most engineers, though, I’d say they’re pretty safe!
I have an exam tomorrow on Fourier Series and I can tell that no Instructor in my college managed to make me understand it this way. Despite the fact that they all have PhDs but its always the way of explanation that matters. Your teaching skills are on another level
That’s what I’m saying all their phd’s are literally useless. Most of them suck so much at teaching, theirs this graduate kid who only has his bachelors and he explains stuff better and seems to have a better understanding of the material then our PhD having Profesor
I'm taking a masters course on Fourier Analysis right now, and rewatching this video just now shows me that the level of (even technical!) essence he manages to address without introducing new jargon is astonishing. Especially considering how long-winded definitions of things like even Cauchy sequences and limits actually are! Around 9' he's actually talking about _Cesàro convergence,_ for instance, something I never saw in a bachelors course. And yet he doesn't miss it! And _still_ he acknowledges that he swept some things under the rug! This is a great man.
3b1b Has allowed me to find beauty (and even a little love for maths) a subject I previously (and kind of still hate/dislike). I've went from barely passing to acing my college math exams, much thanks to the conceptually and visually (yet incredibly accurate) descriptions Grant has given. The overview stipped of the detailed theoretical information is priceless. So much respect to you! Please join his patreon!
I'm an electronic engineer amoung other degrees, and I've mastered the math back in the day and used dfft on quite a few occasions proffesionally but this was a wonder to watch and made me look at it from a new fresh angle. This video should be part of every curiculum that includes fourier transform. The part about how the Fourier got the idea in the first place was especially worthwhile for me. Thank you
If you're interested, you can prove 2isin(x)=e^ix-e^-ix just by looking at the difference vector of the ones shown. It's modulus is 2sin(x) and is vertical thus the vector is 2isin(x).
@@eunhyoukshin7777 This dude has a greater mathematical insight than I ever dream to have, but even though I don't know what he does outside these videos, to call someone a genius for explaining subjects you already encounter in your first year of studying physics or mathematics is a little bit too much.
It is the ultimate high praise to your teaching skills that a video on a complex mathematical subject like this, gets 2.6 million views. Absolutely brilliant.
Physics student here!! Thank you so much for everything you do, your content is SO valuable to me and many other students, I've even had 2 professors send us your videos for better understanding. You are a blessing!:)
You make me love math.After watching one video I go out to relate everything in nature and i almost never fail to find a relation . Math to me now feel like a suject of great wisdom and it is more of a skill when practised for enough times can improve your understanding in it thank you man !
You do such a good job of explaining this. It's been nearly 50 years since I learnt this kind of maths, so I'm a bit rusty on some of it, but I still get the general idea and could rewatch it...plus it's so calm and soothing to watch the drawings happen! 😊
i earlier told how your essence series are in sync with my courses in college ... i studied calculus in 1st sem ... just as your series rolled in . i studied linear algebra in 2nd one ... longside your your series on it . i have to study differential equation for 3rd sem and guess what ... you put out what i exactly need . my core course contains ' fourier series and special function ( gamma , bessel and so on )' and you just bring this gem . i am so lucky .
I have been using Fourier analysis in my work for over 50 years and I was taught the old way in terms of transforms between frequency and time domains. I guess I understand the principles, techniques and math really well, or at least I thought I did until I saw this. This visualisation is truly mind blowing. What a fantastic video and all done in less than half an hour!
The first time I visited this channel, I was: "How on Earth did he make 3.5mil followers?" Now: "How on Earth does he only have 3.5mil followers?" I guess, even for a non math head, this would be a pleasure to watch. Keep them flowing!
I rarely write comments on UA-cam, but right now I am so overwhelmed by your visualization and explanation that I cannot remain silent. I think you are a genius at explaining things like this. Thank you very much for what you are doing.
Please make video about Laplace transform and (or) Z transform, I am sure there a lot of others confused by that topic. And I haven't seen better person to explain it to us
Laplace transforms are for example beautifully used in structural dynamics. It would be nice to see something like that visualised indeed. Not an easy topic to study from text books only lol
Probably my favourite thing about "this side of UA-cam" is how often people will reference each other's channels in odd ways like this. Came looking for a comment about it as soon as I saw it :P
Crazy how we can sometimes detect symbolic styles subconsciously. I wasn’t sure what that logo was at first, thinking it was either for CGP Grey or one of Brady’s channels. Guess I was right on both. Maybe the gear was a giveaway.
This is sick! As usual, painfully clear explanations, and the exercises at the end really helped me to solidify my understanding and to get a feel for the beauty of Fourier series! I couldn't even believe I was actually expressing a discontinuous step function as an infinite sum of trig functions! Thanks for all your hard work Grant, and I'm looking forward to the lecture on the Laplace transform!
0:40 Honestly... it's one of those things that I wasn't sure I'd _ever_ be able to *_truly_* wrap my head around... Like not only _integer_ but *_constant,_* and yet they interfere with eachother in sufficient volume to mess with the image? But honestly thinking about it, it's a rather sensible logical conclusion of a tool so powerful... regardless of how non-obvious it is...
thats not true. he used svg data which was taken from a picture drawn before. he just followed the tracks. so the artist was first and then the program ;P
if you look at it , taylor series is a similar idea of breaking down a function ( must satisfy some conditions first ) to an infinite sum of its derivatives , each amped up a certain amount .
Just want to say you have no idea how inspiring and influential you are to every person that is interested math. Definitely not being the only one, I am greatly delighted, encouraged, and motivated by you on the journal of learning math. Thank you for your contribution, thank you, thank you, thank you.
I can't thank you enough for making this video. I might have watched it a hundred times before I could make sense of the maths behind this beautiful art but when you do understand it, it's so rewarding. People like you willing to teach is why internet still healthy.
this is an amazing video! i'm an engineering intern working with magnetic excitation loops and this explains fourier series so neatly! absolutely amazing visuals and a great explanation for a difficult topic to cover--well done!
You make the most beautifully constructed and animated video's I have ever seen on youtube. Thank you for this blessing! Much love from the Netherlands. :)
I LOVE THIS !!! My brain has never felt more alive. Don't ask me to repeat it all, but the way you explain this actually enabled me to stop the video here and there, and (sort of) predict what you were going to say next. I WANT MOOOOORE !!!
This was breathtaking. I have been becoming hopeless about the world, but now I'm going to see myself as a tiny sine wave contribution to a universal pattern so complex, I'll never see it. And yet: my tiny little contribution matters to the whole. This video might just have brought order and hope to my life. Thank you.
I was in 8th grade when this video came out. over the years I would stumble upon this video and watch and understand it as much as I could up to the point I would understand the math(because I wasn't even aware of some of the topics existing) and end the video there. Now after 5 years, I can proudly say that I have completed the full video fully understanding it, and also making a program similar to what is shown in the video. Thank you for sharing such amazing knowledge with us.
Can we take the time to think of other math videos in general overall : their content, explaination, and surprisingly most importantly -their video effects and animations on their content..... I mean 3b1b takes that to a different level. With his beautiful and precise animations he helps you dive deep into whatever he explains and it's really satisfying You should really be recognised for that .
I was cramming hard to get my brain to recall this stuff, and thankfully found your video again. This is so beautiful and intuitive that everything instantly clicked! Ever grateful for your videos
4:19 the people are (in order) Pythagoras, Euclid, Archimedes, Fermat, Newton, Leibniz, Bernoulli(?), Euler, Fourier, Gauss, Riemann, Cantor(?), Noether(?), Ramanujan, Gödel, Turing. Just for reference, I put a ? besides the ones that may be wrong.
I love how after he explains a concept, i think "Ah, i already heard about that but i can see why i never saw an illustration of the phenomenon: it's so complex !" and then he just proceed to brute-force an complex animation that explain efficiently what the idea is about.
Brilliant video! I was never taught why multiplying by the exponential factor inside the integral was done, and where the reasoning for doing so comes from, but seeing it represented in this way makes it completely intuitive! Wonderful explanation
It's a basic principle of orthogonal functions, although he made an interesting visualization of it here. You were never taught that with Fourier series? Was that in undergrad or graduate?
@@MM3Soapgoblin Well we were exposed to it very briefly in Calc II or III, and then again in real analysis, but it was never really emphasized or used in any way after being introduced, so I just noted that it was a thing, sort of like a change of variables deal. This was during undergrad, and I never once encountered it in a graduate course, though to be fair I was studying the more theoretical side of things, focusing on topology, measure theory, algebra and mathematical logic.
@@trymbruset3868 Huh, interesting. We spent a whole week on orthogonality to setup up the foundation for Fourier (and other) series expansions. It was the first week of our first class in the graduate physics program at UCCS.
11:35 This is the time where I figured out exactly where you were going! You were 100% correct, this was intuitive. Also wanted to say that I appreciate you so much ❤
Not only the style but this incredible calm and... special voice. If someone would exactly do what he did with a normal or "bad" voice: No one would listen to him/her. (crazy thesis)
@@MetapeterUndMetagreta Personally, I never considered his voice. But what's important to me is his clear and easily understandable speech. UA-cam is filled with videos explaining university level mathematics that I could never listen to for the sheer fact that I can't understand the accent. I really appreciate the effort, but a strong accent immediately makes me click away
As a high school student who hasn’t (officially) taken vector calculus yet, this explanation of Fourier series was incredibly well done for someone like me to understand it. The whole series about differential equations has been an adventure opening doors unknown to me in the realm of mathematics, and I’m excited to see what else is out there!
I am also a high school student! I just finished my freshman year but I understand this as well. I am actually going to college for calculus next year, but I actually have already studied it. My introduction to calculus was 2 years ago and I learned it through this youtube channel! I am very happy now that I am more advanced that I have that basic intuition of the math so that whenever I do calculus 1 next year, I won't be confused. When I am an adult, I am definitely going to support this guy because his way of teaching is incredible!
I am a young web developer with poor mathematical skills but I always got fascinated how those .svg files actually draw figures. Although I don't understand anything but seeing arrows moving in circular motion creating a pictures got me goosebumps. Knowledge is power🙏
third year of University, i had to study this and MY GOD the book (combined with my course teachers *nonexistent* teaching skill) made me feel like i was reading hieroglyphs...... *thank* *you* *Grant* *Sanderson* thanks a million...no thanks a billion for making this so easy to understand
I had tears in my eyes as I watched this. The last time I was overwhelmed this bad was in 2011 when I watched Marley and me (doesn't exactly speak highly of me). Beautiful. I'm just overwhelmed with the sheer beauty of everything you shared, thank you.
That's really great. The coefficient being Integral f(t) e^(-n)τi, is well explained here. We had it introduced as a scalar multiplication in a infinite dimensional vector space of Functions which is also cool
I have been teaching FT in this way for years, and I must say that - based on everything I know - this is the most accessible way for students to really *understand* it.
When I grew up using vectors in artistic software (Illustrator, Inkscape, etc), I knew generally that SOME kind of math was telling the vector where to go, but not a clue how they "told" it. When I saw the preview image for this video, I knew where it would go and that I'd finally learn. And I did! It's a bunch of tiny circle-equations all roped together! This is very fun knowledge to have, thank you!
Brilliant work! Your knowledge of the subject is amazing, your teaching ability is phenomenal, and I can't even figure out HOW you made the visuals on this video. Good show!!
I really wish that every intro to Fourier analysis courses/videos/books gave the heat equation/limiting series motivation, and your explanation of transforming the series so that each term is a constant around 19:00 - right at the start of the course. Those two things made the concept feel so much more motivated and transparent. Guess they should all just watch this video!
Let's take this to the logical conclusion: a 3D movie defined as an octonion fourier series. three dimensions for space, three dimensions for color, and two dimensions for audio waveform, exclude the real components. THIS NEEDS TO BE DONE!
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
After listening to a lot of teachers, I have to say that you are simply the best explainer I know. Probably one of the greatest teachers of all time. By explaining complex and powerful ideas in such a beautiful and simple way, your work will surely have a big impact on the life of future scientists and engineers. Keep it going man, you are doing an amazing job!
I have to subtract e to the i times pi from this comment
where did you do your PhD from?
He truly is very good at what he does! You can tell that he has a good understanding of when his explanations are good, and you can tell he takes a lot of time to get to that point.
Completelly agree
I didn't do a PhD in physics and I think the same
Grant, you have the unique trifecta:
1. Intelligence to understand these complex topics.
2. Ability (and willingness!) to explain them clearly.
3. Technical chops to animate and edit your explanations.
Nothing you do is easy but it is all appreciated by a wide audience.
Agreed. He is easily one of the best, if not THE ABSOLUTE BEST
Thanks for adding chops and trifecta to my vocabulary.
That is not a unique trifecta by any stretch of imagination.
Many have it, and more to the point everyone can.
*You* can have that trifecta.
If you don't, that's your own choice.
A lot of Stanford/MIT/UCB etc Computer science graduates have all 3.
There's also a strong instinct for visual beauty, a tendency toward warm communication, and memory/empathy for what it's like to not know the concepts yet, which are what make 3b1b really stand out, IMO
As I begin my journey to get a physics degree, I can't help but look back and thank you for all the content you've made. Truly inspiring and educational stuff :)
Such a generous guy, thanks for supporting this stuff on UA-cam
please give me tips as I also would like to have a degree in physics
@@spongbong0 im innately a curious person, so physics is a pathway for me to understand how things work. Im particularly interested in how things work on a fundamental level and look forward to learning about relativity and QM in depth.
For me, choosing physics is like following a passion; for you, i dont know what physics might be, so take some classes and find out!?
@@lol12313 I've expressed my feelings in that exact same way once. 🤣 I see we have similar feelings
@@lol12313 I want to be an astrophysist please give me some tips on how to get good at physics I practice questions daily but I don't know what else to do
*_Grant, you are the beacon of light in the Math world to me and maybe millions of people around the world._*
You have:
✎Talent to understand the complex principles
✎Passion to share your knowledge and love for math to people
✎Acute competency to explain and animate the concepts into common languages for anyone
✎Persistency and hard work that only few people can sustain
🏆🏆Thank you and thank you!!!
=================================
Also want to give thanks to the founders of UA-cam!
I’m in the process of writing my thesis for a PhD in theoretical physics and I’ll be completely honest, I cried at how elegant this explanation is. Thank you for helping someone who feels they’ve lost a lot of passion for maths and physics after years of hard work, realise that they still have the capacity to really care about these subjects. Truly thank you.
I really admire those who study mathematics and theoretical physics.
What made you lose passion along the way? I just finished my thesis for a PhD in math and I'm still excited about the math itself. Worst parts of academia are still stuff outside the math (grant writing, etc..)
Oh man. Happy for you sir.
@@thesickbeat ya i am annoyed by these type of comments but then i feel bad abt promoting for some1 to not speak what they want
It's been 11 months, how are you going George ? I will you're all good and healthy ^^
Math is even more beautiful when someone teach like this.
Yes, i agree.
Teaches*
Yeah it almost becomes sexy.
@@itsawonderfullife4802 Almost?!? 😉
I was your 1200th liker
I dropped out in 10th grade 25 years ago and your videos have inspired me to go back to school.
It's never too late!
u just dont learn that in school but in uni. indeed, hes a great lecturer
Amir, I'm about your age and just finishing a bachelor's degree... If I can, you can... And one of my favorite math teachers is also named A. Ghoreishi. :)
How do you go back anyways idk how it works
@@skydragon3857 Look for a local college/university, visit their web-site and find the apply button... Also, look for non-traditional student services for help, advice and support.
Somehow this wound up in my recommended, and I’ll be frank here. I’m in 10th grade and am nowhere NEAR the level of algebra and calculus comprehension required for this, but you explained this complex subject so well and fluently and thoroughly that even I managed to roughly understand some of the concepts! Excellent work, and keep it up!
I (a Junior Electrical Engineering Student) went through the same experience time and time again. But, remembering these after a time of learning is a great way to see how far you have come with understanding and knowledge; I did that as I was watching this because I’m going over Fourier Series right now in my Signals and Linear systems class, and I said to myself “wow, I’ve learned a lot, I actually understand where these are coming from!” when I watched this last year, I had no idea where things were coming from, but after learning about the fundamental concepts and applying them, the fog cleared and I actually recognized things. All of this to say, always go back to videos like this to see what you recognize to see what you now know - it’s the joy of learning.
Agreed. How in the world did I just receive that when I'm mathematically illiterate yet artfully wired?
@@andiehammettz4u265 Because there is an art to mathematics, art comes from mathematics in the end as it describes everything in the universe
@@foxphire0093 but when I draw I'm not thinking of a formula. The creativity is not pre formulated outside of how the parts relating to the whole. Form AND function.
i’m a sophomore too and i’ve just been watching a bunch of his random videos and i watched this one like a couple weeks ago lol
I’m imagining students watching this and furiously taking notes while I’m here at 2am thinking “oooh circles make shapes”
Most average students: "well it is 3am for me"
i'm bad at math ;-;
well it is 3 am right now here
This video came out while I was taking my intro diff EQ class. Didn't see it till now at 3am. Would have been helpful at the time since my Prof gave zero context for how these equations work and how they can be applied.
Ok
This is pure gold for an engineering student like myself. I hope you one day get the recognition you truly deserve for illustrating the ideas this beautifully and clean. Thank you.
same for me... as an engineering student, i've never fully understood the math behind Fourier, limiting myself to apply it mechanically. I know what an FFT and the Fourier series are built for and their importance in signal processing, but the math behind them remains for me some sort of magic even after Math III exam.
This, damn this is totally mind blowing.
What an amazing explanation, this video deserves 10 million views!
Not 10 million but 20 million
Aight, hold on lemme watch 6.5 million times
Does everyone really need to know what a fourier series is
No , it deserves 10000000000000 Trillion views and 10000000000000000000000000000000Trillion subscribers
@@jerryboy9652 even more... 10000 BILLION VIEWS
I am a Math Ph.D holder who's been both teaching and researching the Fourier related field and, HOLY CRAP this is one of the best visual explanation I've seen. I will definitely distribute a reference to this channel wherever I will go.
mr Grant is a genius teacher!!!
The mathematics for Alfred Hitchcock, cartoon drawing, is about the same as a diamond Anvil.
Joseph Fourier must be so proud to have a Fourier-portrait of himself
And when it's built up from frequency components one at a time, it kind of looks like he's developing from an embryo!
That must have been some hard-core editing
Thanks for the great content
Animating ≠ Editing
Doing something like this with video editing software is almost impossible. Each of his videos is entirely produced by a Python program that uses a library he wrote (which is also open source IIRC). I guess that is the only sane way to create videos like this.
@@giacomo.delazzari still pretty insane
Hard-core coding instead.
@@giacomo.delazzari yep, it's online: github.com/3b1b/manim
After watching this for the 1000th time, I finally had the key intuition necessary to code my own Fourier Transform. As a musician, nothing makes me happier than having my own little Fourier transform now. I just want to thank you for these videos, they’ve completely resparked my joy for math.
So you've coded your very own Melodyne?
@@dracovet777 Sort of lol. Melodyne is way more intense than my algorithm. Since I wrote this I've managed to optimize it using some linear algebra I just learned, but it's still just a basic fourier transform and not anywhere close to an fft
Could you tell me how you coded it? I would love to try!
@@sidewinded1 ok so I use python’s numpy library. Long story short I take the inner product of 2 vectors which are representative of the functions you get in the Fourier series. The fancy stuff is making it all compact so I can use it wherever I need to, I basically made that all into a lambda function. I know this isn’t the worlds best explanation but all I’m trying to say is it boils down to how much linear algebra you know.
Nothing makes you happier? No wife?
It's amazing to see all these concepts described with animated drawings. I find it even more amazing that generations of people were able to learn and apply the concepts well before the advent of moving pictures. To really internalize these ideas and visualize these things in your mind must be an amazing experience.
Your visualization skills alone deserve a Nobel prize :O
*field
*field
Nobel prize for optics?
@@hellofromc-1374: as in Fields Medal? Indeed.
Agreee👍👍
that list of immortal mathematicians is imcomplete
it doesn't have you in it
Link one research paper this guy has published..?
Do you even know his name without looking it up lol
@@48956l so you really thought he genuinely wanted 3b1b's name in it? Really?
Shiva Kumar ya and ur name belongs on the immortal dumbasses list
That, I guess, would be an overestimation but I have to admit that he knows what he is doing
Because he's not a mathematician, he's an educator.
I'm a seismologist and even I don't understand Fourier theory at this level of ease and intuition. You took one of the most complicated concepts in science and made it so beautiful and intuitive.
The global academic ecosystem needs more people like 3Blue1Brown to teach Maths to students.
can't you just say "students" instead of all you wrote at the beginning?
"Taylor made polynomial" and then not acknowledging the pun, I love it
Hahaha I caught it too xD
3:45
I dont get it. Can you plz explain.:(
@@c4stmiranda902basically, you can express many functions locally as an infinite polynomial or power series called a *Taylor* series.
@@c4stmiranda902 he has another video about Taylor series:
ua-cam.com/video/3d6DsjIBzJ4/v-deo.html
In all my years at college, I've never seen such a stunning presentation about Fourier series. I can't help but say thank you . This is in a total different level of explanation...
Whoever first invents a time machine, please go back in time and show Fourier this video. Absolutely amazing!
Fourier would be proud.
@@dexter2392 Or , he will create the fourires series because of the video
@@chupetaparabose1 Maybe he made this series because of this comment :3
Imagine how he visualised this inside his head back in 1800s.
@@FiasaPower I was wondering the same... What a genius could imagine this?
Amazing minds.
I've never known what even is a "differential equation", and I'm definitely never studying this kind of advanced maths in college. However, this is one of the best youtube series I've ever seen, and this super well-articulated, extremely elegant video has prompted me to express my utmost appreciation for your content, Mr. Sanderson. Truly the best Maths channel in the world.
I took courses on signal & system and digital signal processing before UA-cam was founded. I wish I was born later so I could take advantage of the best explainers like you and the best of visual presentations like this. The timings of items you throw on the screen, the sequence, the connections, and the visual ques you use is beyond precision, beyond exact. This is a God-mode representation of Fourier series in terms of rotating circles! Take a bow!
I’m in Signals right now and watching this definitely helps my overall understanding of why things happen as opposed to just accepting it and moving on
Okay. Grant Sanderson is the best math youtuber hands down. It's surreal that you can relate to so many concepts with just the Fourier series.
I am an electronic engineer. I took a dozen of courses about Fourier series and transform. I work with spectral analysis on daily basis and this video blew my mind
Same here, though I only apply dfft occasionally in my professional life.
Awesome content
I've finished a 5-year degree of applied physics, but I gotta say that I never quite fully understood why the Fourier series works. A big reason for that is that there's so many things to learn that you mostly learn the 'how' instead of the 'why'. It makes for quick gains of knowledge, but it simultaneously makes for quick losses of knowledge, as it really is the 'why' that makes for the building blocks of knowledge in the long run.
Your channel, and especially this video, masterfully compresses the 'why' into its central components and makes for quick and stable gains of knowledge. In the long run, you will have helped creating a much more efficient, robust and accessible education for everyone. Great job, and keep going!
conacal rubdur it’s a very broad engineering degree (I should probably have written Engineering physics, as that’s its real name), so you can get into most engineering things (except for chemistry, I guess) if you choose the right specialization (i.e. Master’s degree). I myself am working with software development and machine learning!
conacal rubdur Yes, it is computer science! I’d say that more and more engineers go into this field nowadays, despite coming from quite different backgrounds in their bachelor’s. As you might realize, my Engineering physics degree was quite different from what I’m working with now. Basically, my first 3 years (i.e. bachelor’s) consisted of lots of heavy maths and physics, which has given me a solid mathematical foundation to understand most research papers I read on AI and other subjects. In your case, I’d say that most engineering degrees give a good mathematical foundation, though (except maybe for chemical engineering; I don’t know how complicated maths needs to be there), so it’s probably more important to choose a bachelor’s that you could feel motivated for, rather than choosing something that could boost your career.
Anyways, owing to your list of subjects, I’d say that mechanical or aerospace engineering would probably be the best bet! I think bachelor’s = undergrad, so you have to decide on your bachelor’s before you get into college. Don’t worry though; the math you learn in one field is often used in the next (such as fourier series), so choosing one specialization doesn’t mean you can’t change your mind in the future! :)
conacal rubdur Yeah, I’d go for mechanical engineering in that case, since it’s broader and, who knows, maybe you’ll find something else that’s more interesting there, and then it’s nice to know that your broad education gives you better opportunities to specialize in that if you want!
I have no idea what the chances of landing the jobs you’re listing are, and I’d definitely say that it depends on where you are. Engineers are pretty popular on the job market though, so finding a job shouldn’t be that hard.
Regarding the major, I’d say that it also depends on where you are. I’ve heard that in U.S. it’s pretty common to do a bachelor’s work for a while, and then get back to a master’s. Many here hope that the company offers a paid master’s, since doing it on your own very likely costs more than you get back from a future career. In Europe, however, the situation is very different, as we don’t have to pay for each semester. Therefore, we often do a bachelor’s and master’s consecutively, without a break, in order to actually finish our degree. I myself would reason that if I started working after my bachelor’s, I wouldn’t wanna go back to school once I’ve settled into this new lifestyle of getting paid and not having a constant feeling that I have to study. People are of course different, but if you’re in Europe, I’d recommend bachelor’s + master’s in one go, since you then finish everything in one go, and it feels like you continuously improve your lifestyle!
conacal rubdur well, location matters in the sense that your society works differently than in Europe. For you, it costs a whole lot more for each additional semester you study; whilst in Europe, you don’t have that much to lose to study a couple more years. Regarding your question about applying for jobs all over US, I don’t know what’s best, since I don’t live there and don’t know anything about the costs of travelling or how valuable it is to move for jobs there. If it had been me, though, I would have started out looking for jobs nearby, since it’s simpler!
conacal rubdur Yes, that sounds good! Those unemployment rates are very low, so you shouldn’t worry about that. Additionally, if I were to worry about unemployment after graduation, I would take into consideration how easy my job is to automate, since that is a trend that will accelerate. For most engineers, though, I’d say they’re pretty safe!
This video is being recommended to me by my university maths department!
All the best from Berlin! Awesome work
Digitalisierung be like
Wie geht es deutschen Hochschulen?
I have an exam tomorrow on Fourier Series and I can tell that no Instructor in my college managed to make me understand it this way.
Despite the fact that they all have PhDs but its always the way of explanation that matters.
Your teaching skills are on another level
Bruh ok, did i ask?
@Santino EGL ik, and urs not
@@toxickid2456 no one cares what you think
@@eigenrauflinog9069 Who asked?
That’s what I’m saying all their phd’s are literally useless. Most of them suck so much at teaching, theirs this graduate kid who only has his bachelors and he explains stuff better and seems to have a better understanding of the material then our PhD having Profesor
Thanks!
I'm taking a masters course on Fourier Analysis right now, and rewatching this video just now shows me that the level of (even technical!) essence he manages to address without introducing new jargon is astonishing. Especially considering how long-winded definitions of things like even Cauchy sequences and limits actually are! Around 9' he's actually talking about _Cesàro convergence,_ for instance, something I never saw in a bachelors course. And yet he doesn't miss it! And _still_ he acknowledges that he swept some things under the rug!
This is a great man.
3b1b Has allowed me to find beauty (and even a little love for maths) a subject I previously (and kind of still hate/dislike). I've went from barely passing to acing my college math exams, much thanks to the conceptually and visually (yet incredibly accurate) descriptions Grant has given. The overview stipped of the detailed theoretical information is priceless. So much respect to you! Please join his patreon!
I'd say he Grant-ed you the insight you needed.
@@denelson83 Who Grant-ed you the permission to make such puns?
@@sadkritx6200 joe
Kk
@Aaditya Sabharwal you know
I'm an electronic engineer amoung other degrees, and I've mastered the math back in the day and used dfft on quite a few occasions proffesionally but this was a wonder to watch and made me look at it from a new fresh angle. This video should be part of every curiculum that includes fourier transform. The part about how the Fourier got the idea in the first place was especially worthwhile for me. Thank you
Exactly. It's like I've been doing the math blindly, but this gives me an opportunity to actually see what I've been doing.
Uii
10:08, a beautifully wordless proof of e^-ix + e^ix = 2 cos(x). Thank you for this!
i actually didnt think about that, ur a smart guy
If you're interested, you can prove 2isin(x)=e^ix-e^-ix just by looking at the difference vector of the ones shown. It's modulus is 2sin(x) and is vertical thus the vector is 2isin(x).
Every youtube science channel recently: draws these fourier shapes with a couple of arrows on screen
3Blue1Brown: hold my beer
When a mathematical genius is also a programming genius:
@@eunhyoukshin7777 This dude has a greater mathematical insight than I ever dream to have, but even though I don't know what he does outside these videos, to call someone a genius for explaining subjects you already encounter in your first year of studying physics or mathematics is a little bit too much.
It is the ultimate high praise to your teaching skills that a video on a complex mathematical subject like this, gets 2.6 million views. Absolutely brilliant.
10 million views 😅
Physics student here!! Thank you so much for everything you do, your content is SO valuable to me and many other students, I've even had 2 professors send us your videos for better understanding. You are a blessing!:)
"ah shit, here we go again"
-me about to spend the next indefinite amount of time pondering maths
LOL That's me exactly! :D
wow. congrats on your world changing comment
Begins grinding gears.
there goes sleeping
You make me love math.After watching one video I go out to relate everything in nature and i almost never fail to find a relation . Math to me now feel like a suject of great wisdom and it is more of a skill when practised for enough times can improve your understanding in it thank you man !
You do such a good job of explaining this. It's been nearly 50 years since I learnt this kind of maths, so I'm a bit rusty on some of it, but I still get the general idea and could rewatch it...plus it's so calm and soothing to watch the drawings happen! 😊
I feel privileged to discover this channel even before my college begins
Just luck + time
Yes you are. Make the most of it. Enjoy learning. Very happy for you
i earlier told how your essence series are in sync with my courses in college ...
i studied calculus in 1st sem ... just as your series rolled in .
i studied linear algebra in 2nd one ... longside your your series on it .
i have to study differential equation for 3rd sem and guess what ... you put out what i exactly need .
my core course contains ' fourier series and special function ( gamma , bessel and so on )' and you just bring this gem .
i am so lucky .
Wish I was, I always just miss them :/
I have been using Fourier analysis in my work for over 50 years and I was taught the old way in terms of transforms between frequency and time domains. I guess I understand the principles, techniques and math really well, or at least I thought I did until I saw this. This visualisation is truly mind blowing. What a fantastic video and all done in less than half an hour!
The first time I visited this channel, I was: "How on Earth did he make 3.5mil followers?"
Now: "How on Earth does he only have 3.5mil followers?"
I guess, even for a non math head, this would be a pleasure to watch.
Keep them flowing!
He now have more subscribers (followers) than Numberphile.
I rarely write comments on UA-cam, but right now I am so overwhelmed by your visualization and explanation that I cannot remain silent. I think you are a genius at explaining things like this. Thank you very much for what you are doing.
The calmness of your voice, the music in the background, and the fluidity of the animation make watching this really soothing. It's also beautiful.
i don’t understand a thing about this video but your voice is just so soothing and it makes me want to keep watching
Please make video about Laplace transform and (or) Z transform, I am sure there a lot of others confused by that topic. And I haven't seen better person to explain it to us
Yes, that would be a very interesting topic!
i believe he mentioned in an earlier video that he will explain them in a later video of this series
Yes! I have so much trouble visualising those
@@thomas.02 oh that's nice, I am looking forward to it!
Laplace transforms are for example beautifully used in structural dynamics. It would be nice to see something like that visualised indeed. Not an easy topic to study from text books only lol
0:25 That's the Nail and Gear of HELLO INTERNET!
I was pleasantly surprised when I saw it too! Great Easter egg!
And hello Tims!
Probably my favourite thing about "this side of UA-cam" is how often people will reference each other's channels in odd ways like this. Came looking for a comment about it as soon as I saw it :P
Yes - this Tim noticed it too and was delighted! :-)
Crazy how we can sometimes detect symbolic styles subconsciously. I wasn’t sure what that logo was at first, thinking it was either for CGP Grey or one of Brady’s channels. Guess I was right on both. Maybe the gear was a giveaway.
This is sick! As usual, painfully clear explanations, and the exercises at the end really helped me to solidify my understanding and to get a feel for the beauty of Fourier series! I couldn't even believe I was actually expressing a discontinuous step function as an infinite sum of trig functions! Thanks for all your hard work Grant, and I'm looking forward to the lecture on the Laplace transform!
0:40
Honestly... it's one of those things that I wasn't sure I'd _ever_ be able to *_truly_* wrap my head around... Like not only _integer_ but *_constant,_* and yet they interfere with eachother in sufficient volume to mess with the image?
But honestly thinking about it, it's a rather sensible logical conclusion of a tool so powerful... regardless of how non-obvious it is...
Explanations like this 20:09 are the reason I love this channel
My jaw dropped when I got there. I've been looking for a way to understand that concept for years.
Yeah its much better than just stating orthogonality of sinusoidals
True
same here!
That moment when Rotating vectors draw better than you 😑
Such is the power of math
i feel your pain
Maybe you're not rotating enough when drawing something
thats not true. he used svg data which was taken from a picture drawn before. he just followed the tracks. so the artist was first and then the program ;P
@@DarthZackTheFirstI you killed this poor little joke, how dare you!
3:45 Fourier-made, not Taylor-made. :P
I'm a little upset that I got beaten to this
Damn you, I already made that joke on the patreon draft. Don't you go stealing my puns!
I usually hate puns, but this one...
if you look at it , taylor series is a similar idea of breaking down a function ( must satisfy some conditions first ) to an infinite sum of its derivatives , each amped up a certain amount .
I thought that was an actual mistake while watching it, then realized tailor-made
Just want to say you have no idea how inspiring and influential you are to every person that is interested math. Definitely not being the only one, I am greatly delighted, encouraged, and motivated by you on the journal of learning math. Thank you for your contribution, thank you, thank you, thank you.
This is actually the greatest channel on UA-cam
friend: how well can you draw?
me: how many arrows you got?
friend has left the chat
100th like
jemma??
Thi is why you and I have no friends. 😢
lol
beautiful! But how do you add colour and shade to the last arrow? In that sense the arrows don't draw as the points are invisible until....
I can't thank you enough for making this video. I might have watched it a hundred times before I could make sense of the maths behind this beautiful art but when you do understand it, it's so rewarding. People like you willing to teach is why internet still healthy.
Guys I think I got it
Those at the start are circles
Hugh Dennis answering Picture of the Week on Mock the Week:
"That's Boris Johnson."
Actually they are circumferences
@@vampyricon7026 Oh, no. I'm not brave enough for politics.
Whats a circle?
👏👏👏👏👏👏👏👏👏👏👏
Fourier and Laplace were basically the only two things I got out of higher level calc. I love your animiations by the way!
I studied them but don't remember anything :(
this is an amazing video! i'm an engineering intern working with magnetic excitation loops and this explains fourier series so neatly! absolutely amazing visuals and a great explanation for a difficult topic to cover--well done!
The work and genius that goes into making this video make it a true piece of art.
You make the most beautifully constructed and animated video's I have ever seen on youtube. Thank you for this blessing! Much love from the Netherlands. :)
I LOVE THIS !!!
My brain has never felt more alive.
Don't ask me to repeat it all, but the way you explain this actually enabled me to stop the video here and there, and (sort of) predict what you were going to say next.
I WANT MOOOOORE !!!
This was breathtaking.
I have been becoming hopeless about the world, but now I'm going to see myself as a tiny sine wave contribution to a universal pattern so complex, I'll never see it. And yet: my tiny little contribution matters to the whole.
This video might just have brought order and hope to my life.
Thank you.
I was in 8th grade when this video came out. over the years I would stumble upon this video and watch and understand it as much as I could up to the point I would understand the math(because I wasn't even aware of some of the topics existing) and end the video there. Now after 5 years, I can proudly say that I have completed the full video fully understanding it, and also making a program similar to what is shown in the video. Thank you for sharing such amazing knowledge with us.
me in the beginning of video: "Time to get smarter!"
me halfway through: "Oh look the circles! it draws da picture! :O"
So you succeeded!
I have no idea what any of this means. But it's so beautifully explained and satisfying to watch, that I can't.... stop.... watching
I truly enjoyed seeing this generalization. It had never dawned on me to use a 2-d curve as input to the DFT. Way to go.
18:50 this kind of gave me a deeper intuition on the fourier transform; thank you.
being a visual learner I never really understood Fourier series. This is amazingly helpful!
Your not alone...
Everybody is a visual learner, you just gotta think hard to visualize what formulas mean
Abstract thinkers (3D) use more visual than Straight thinkers (2D)...
Seriously 3B1B had reached math education immortality
Taking 2D Concepts and turning them into 3D Concepts is what this Video is about at least in my mind. Left Brain Right Brain...
You were expecting trigonometric functions but it was I, complex exponential!
Euler's equation is just so fundamentally beautiful. It is superior.
@@randomaccessfemale superior to what?
*Evil sound plays in background*
trigonometric functions’ bizarre adventure
Twas i!
Can we take the time to think of other math videos in general overall : their content, explaination, and surprisingly most importantly -their video effects and animations on their content.....
I mean 3b1b takes that to a different level. With his beautiful and precise animations he helps you dive deep into whatever he explains and it's really satisfying
You should really be recognised for that .
I was cramming hard to get my brain to recall this stuff, and thankfully found your video again.
This is so beautiful and intuitive that everything instantly clicked! Ever grateful for your videos
4:19 the people are (in order) Pythagoras, Euclid, Archimedes, Fermat, Newton, Leibniz, Bernoulli(?), Euler, Fourier, Gauss, Riemann, Cantor(?), Noether(?), Ramanujan,
Gödel, Turing.
Just for reference, I put a ? besides the ones that may be wrong.
No Taylor, Lagrange, Descartes and Pascal? Damn...
Shamefully missing Thales among the immortals as well. Video dropped from 10/10 to a 9.5/10 just for that.
Yes, that is Emmy Noether
I thought that fat dude was JS Bach
Ok
I love how after he explains a concept, i think "Ah, i already heard about that but i can see why i never saw an illustration of the phenomenon: it's so complex !" and then he just proceed to brute-force an complex animation that explain efficiently what the idea is about.
Brilliant video! I was never taught why multiplying by the exponential factor inside the integral was done, and where the reasoning for doing so comes from, but seeing it represented in this way makes it completely intuitive! Wonderful explanation
It's a basic principle of orthogonal functions, although he made an interesting visualization of it here. You were never taught that with Fourier series? Was that in undergrad or graduate?
@@MM3Soapgoblin Well we were exposed to it very briefly in Calc II or III, and then again in real analysis, but it was never really emphasized or used in any way after being introduced, so I just noted that it was a thing, sort of like a change of variables deal. This was during undergrad, and I never once encountered it in a graduate course, though to be fair I was studying the more theoretical side of things, focusing on topology, measure theory, algebra and mathematical logic.
@@trymbruset3868 Huh, interesting. We spent a whole week on orthogonality to setup up the foundation for Fourier (and other) series expansions. It was the first week of our first class in the graduate physics program at UCCS.
11:35
This is the time where I figured out exactly where you were going! You were 100% correct, this was intuitive.
Also wanted to say that I appreciate you so much ❤
Your explanations beat anything by any other content creators... You are literally god level.
3:45 Taylor-made? I thought we were discussing the Fourier-series?
cheeky. very cheeky.
Nice.
take a complex Taylor series, and restrict it to the unit circle--and you get a Fourier series (with only "positive" modes-counterclockwise rotation).
I just cannot appreciate enough how good the animations are in these videos! MASSIVE respect!!
You now have a Taylor-made solution... you had me
I’m sure I’m not the only fully trained mathematician who watches 3B1B purely out of appreciation for his teaching style.
Not only the style but this incredible calm and... special voice. If someone would exactly do what he did with a normal or "bad" voice: No one would listen to him/her. (crazy thesis)
@@MetapeterUndMetagreta Personally, I never considered his voice. But what's important to me is his clear and easily understandable speech. UA-cam is filled with videos explaining university level mathematics that I could never listen to for the sheer fact that I can't understand the accent. I really appreciate the effort, but a strong accent immediately makes me click away
As a high school student who hasn’t (officially) taken vector calculus yet, this explanation of Fourier series was incredibly well done for someone like me to understand it. The whole series about differential equations has been an adventure opening doors unknown to me in the realm of mathematics, and I’m excited to see what else is out there!
I am also a high school student! I just finished my freshman year but I understand this as well. I am actually going to college for calculus next year, but I actually have already studied it. My introduction to calculus was 2 years ago and I learned it through this youtube channel! I am very happy now that I am more advanced that I have that basic intuition of the math so that whenever I do calculus 1 next year, I won't be confused. When I am an adult, I am definitely going to support this guy because his way of teaching is incredible!
I am a young web developer with poor mathematical skills but I always got fascinated how those .svg files actually draw figures. Although I don't understand anything but seeing arrows moving in circular motion creating a pictures got me goosebumps.
Knowledge is power🙏
I've been looking forward to this
third year of University, i had to study this and MY GOD the book (combined with my course teachers *nonexistent* teaching skill) made me feel like i was reading hieroglyphs...... *thank* *you* *Grant* *Sanderson* thanks a million...no thanks a billion for making this so easy to understand
I had tears in my eyes as I watched this. The last time I was overwhelmed this bad was in 2011 when I watched Marley and me (doesn't exactly speak highly of me). Beautiful. I'm just overwhelmed with the sheer beauty of everything you shared, thank you.
That's really great. The coefficient being Integral f(t) e^(-n)τi, is well explained here. We had it introduced as a scalar multiplication in a infinite dimensional vector space of Functions which is also cool
I have been teaching FT in this way for years, and I must say that - based on everything I know - this is the most accessible way for students to really *understand* it.
What an elegant and clear explanation. And the effectiveness of your visuals CANNOT be understated! Fantastic video
Amazing explanation. It made Fourier series way more interesting than the ones in books
When I grew up using vectors in artistic software (Illustrator, Inkscape, etc), I knew generally that SOME kind of math was telling the vector where to go, but not a clue how they "told" it. When I saw the preview image for this video, I knew where it would go and that I'd finally learn. And I did! It's a bunch of tiny circle-equations all roped together! This is very fun knowledge to have, thank you!
Those actually use Bezier curves, not Fourier series
@@HilbertXVI ah yup, I saw the new videos! You are correct, those are Bezier curves in those programs. Thanks for the heads up!
Brilliant work! Your knowledge of the subject is amazing, your teaching ability is phenomenal, and I can't even figure out HOW you made the visuals on this video. Good show!!
He wrote a program called "manim", it's on GitHub ^^
I really wish that every intro to Fourier analysis courses/videos/books gave the heat equation/limiting series motivation, and your explanation of transforming the series so that each term is a constant around 19:00 - right at the start of the course. Those two things made the concept feel so much more motivated and transparent. Guess they should all just watch this video!
If my teacher ever asks me again to draw something without letting the pencil not touch the paper, ill ignore it and say i was using imaginary numbers
In addition to a great source of learning, your videos are a true source of visual satisfaction.
If a pile of Fourier series can draw one picture, it can draw a sequence of pictures. When is the anime coming out?
Dont talk about the anime when you haven't read the manga
@@ghostofpop what if the anime doesn't have a manga?
@@shayanmoosavi9139 It has light novels though.
Let's take this to the logical conclusion: a 3D movie defined as an octonion fourier series. three dimensions for space, three dimensions for color, and two dimensions for audio waveform, exclude the real components. THIS NEEDS TO BE DONE!
@@Whimsical_Realist You gotta start it! Let us know your progress