I'm genuinely jealous of the next generation of students who will have these videos to introduce them to calculus. The understanding and intuition they bring to a newcomer must be really exciting.

@eduardocortez476

7 жыл бұрын

Devin Neal It is!

@JannikPitt

7 жыл бұрын

I was first exposed to Linear Algebra by his video series. It really got me hooked and I looked forward to every video curious about how the subject will evolve. That was really awesome! I bought some books on mathematics and self-studied maths quite a lot since then.

@adamcummings20

7 жыл бұрын

I'm going into a-level further mathematics next year after GCSE and I am so grateful that this guy does what he does so well

@omamba5105

7 жыл бұрын

They're exciting for me as well, and I really enjoyed calculus back in high school.

@lizardbaron3727

7 жыл бұрын

Devin Neal they're very exciting

"I would use the letter "d" for distance, but that guy has another full time job in Calculus" Lmao

@gregorybattis9588

4 жыл бұрын

I was thinking I was the only one who would laugh at that.

@rka8215

4 жыл бұрын

Isn`t "d" a minor? Isn`t it illegal to make children work full time?

@rka8215

4 жыл бұрын

@@teeraxgaming Isn`t "d" "D`s" son?

@rka8215

4 жыл бұрын

@@teeraxgaming Save the children!

@rka8215

4 жыл бұрын

@@teeraxgaming Why??? Are you kidding? Because 1. They give young parents extra time at night. 2. They make middle aged parents go back to calculus! 3. They keep mature parents from buying a Porsche or a villa in Italy and invest their money in college tuition. 4. They help old parents formulating their last will. 5. And they keep pediatricians happy. That`s why!

When I watched this years and years ago I fell in love with maths again, now I'm a maths teacher and I'm passing this down to my students. I'm so grateful for your channel and I hope you understand these are more than just KZread videos, they mean a lot to people.

@3blue1brown

Жыл бұрын

That's incredibly touching to hear, thanks for sharing!

@divy-07

Жыл бұрын

​​@@3blue1brown respect for replying after 6 years since the post date

@theseangle

4 ай бұрын

Just imagine being 3Blue1Brown and reading such comments from time to time. Just imagine.

@shivendrasingh6136

Ай бұрын

​@@3blue1brown Grant, It was just wow ❤❤... Since you've got this exceptional talent of explaining and animating So why not try some topics like The Essence of complex no....

0: Oh? You're approaching me? dt: I can't beat the shit out of you without getting closer

@sadkritx6200

3 жыл бұрын

0 : Oh ho, then come as close as you like...

@RummanNaser

3 жыл бұрын

I love this community. Making jojokes on maths xD

@rohankishibe8259

2 жыл бұрын

JoJo references on maths related topics is something i expected when certain zeppeli started using the golden ration on us mortals, then mr Jonathan started flexing his spin.

@bluebrowney251

2 жыл бұрын

This was hilarious

@felixgutierrez993

2 жыл бұрын

Oh shid I never thought my JoJo fascination was gonna follow me here in Calculus 🤣

That's it, I'm promoting this channel wherever I find people who say " I'm really not a math person"

@uzairakram899

4 жыл бұрын

I had the same idea but some people are really not into it.

@joshtipton7417

4 жыл бұрын

I was 'not a math person' in high school because I had a crappy understanding of algebra and equations, but always excelled at the theory stuff regardless. I eat videos like this up because you learn all the theory and abstractions that show how cool math can be, but someone else crunches the numbers for you. They should really use this as learning material in schools, it could help a lot of students like me.

@Zivlix

4 жыл бұрын

Josh Tipton as a person like you who loves theory and abstraction but not so good at number crunching but is about to be put into the meat grinder of high school math I cannot say how much I am glad to be at this point of history, a point at which pure math and implied math begin to cross along with so many people and resources to help me to grow my understanding. If you have not then I recommend this video - kzread.info/dash/bejne/gaF-j5Z7XdC5Xbw.html

@dimdenEFF

4 жыл бұрын

I'm really not a math person and I don't understand it ;_;

@tejpatel5320

4 жыл бұрын

I think you will be surprised at how much someone would still dig in their heels. Learned helplessness is a very deep hole made be habit of thought and preconceptions of their ability and of the subject matter.

Grant, I don't think I've ever watched a 20 minute math video and wished there was more. You are super talented, and I want to thank you for releasing this to the world for free. This is not just math. This is art.

@petercoool

6 жыл бұрын

ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ He is Dr. Art

@francescosorce5189

5 жыл бұрын

Math is art, and he's an artist

@joaquinmela5781

5 жыл бұрын

His videos are just so awesome that I'm gonna cry

@aniketh_99

5 жыл бұрын

I want to like this but you have a perfect number of likes and I’d rather not break it

@hziebicki

5 жыл бұрын

Math is art. And art is math.

watching this series has made me fundamentally question the quality of the education I received at school growing up. It's exposed how badly we were explained these concepts in class. I did so much calculus at school without ever being given a real understanding of what i was doing. And then I wonder if the same maybe applies to all my subjects at school. maybe my whole education was actually entirely sub par and I've fallen far short of my potential as a result lol.

@robinlarsson2108

3 жыл бұрын

Welcome to humanity!

@imperialeagle564

3 жыл бұрын

@Mr Right yeah thats very right mr right

@tolep

2 жыл бұрын

@Mr Right Also, watching this, people are relaxed, can pause and replay etc.

@DMahalko

2 жыл бұрын

@Mr Right It should be possible for 12 year-olds who think they have all the answers to go out and get a job, an apartment, etc. If they want to continue their education later as an adult, it is still available and fully paid like grade school was.

@wallacegrommet9343

2 жыл бұрын

Your teachers were mediocre and apathetic

everyone: "no one can calculate instantaneous change. it's totally nonsensical" fathers of calculus: "so I'm gonna do what's called a Pro Gamer Move-"

@deedewald1707

3 жыл бұрын

The art of problem solving is solved here, no problem to show !

@RF-fi2pt

3 жыл бұрын

Wrong. Makes sense so well as work at derivative. See My 3 years ago post, also i posted at keystone video about paradox of derivative.

@Brahvim

3 жыл бұрын

*Pro Mathermatician move

@user-yj8uv7gi3o

2 жыл бұрын

@@Brahvim *Pro Mathematician Move

@Brahvim

2 жыл бұрын

This comment is now 2 months old, thanks for the correction, @@user-yj8uv7gi3o 😂👍 (Saw this after 3 hours :|)

Those "ohhhhhhh, aha!" *click* moments that were so rare in my University calculus classes are so frequent in these videos.

@methatis3013

5 жыл бұрын

University? I thought you learn this in 3rd grade of highschool. Im in 8th grade rn. Do I srsly have to wait 5 more years for this?

@primalforlorn

5 жыл бұрын

@@methatis3013 Not everyone has American style of education system, Calculus is elective in my country for example

@RajShekhar-jy2zi

5 жыл бұрын

@@methatis3013 i study this in 11th class in india .

@Georgexb

5 жыл бұрын

PrimalForlorn In the UK, calculus is introduced in sixth form (year 12), but of course it carries on to university level

@Anonimowany1

4 жыл бұрын

WIsh I had all these KZread Videos when I was still at school like 10-5 years ago. I loved math and physics. (I studied math and physics at the university afterwards) The way those subjects were taught at school was plain and super boring. All these videos on KZread are so fun and I learn even now from all these. I believe in the next decade or so - some really clever minds will arise - smarter than Einstein and Stephen Hawking and all others. Just due to the fact the way all the knowledge is provided and super easy to learn and visualize with the current age of technology. It literally wasnt like that even just a few years ago. The future is looking bright.

Grant, I'm a 39 yo man in the verge of changing my carrier from the Ad industry to the Dev and AI realm. I really wanna thank you for your overwhelmingly great work. This video, oddly enough, changed my life, and I'll forever remember you as a positive force for this change. Thank you very much.

@user-zd3kt5qc7i

5 жыл бұрын

Ad AI.wow

@GeodesicBruh

5 жыл бұрын

You could almost say that after this video the derivative of your feelings with respect to time is positive

@ritageraghty4404

5 жыл бұрын

I am 53 and I am just relearning maths as a hobby. I'm doing it for 3D art and animation including physics simulations that require maths.

@rahulupadhyay3570

4 жыл бұрын

All the best

@krisjaniskalans3474

4 жыл бұрын

man this is fucking powerful

Thank you for the great quality videos. It makes things easy to understand.

@mainconman2201

Жыл бұрын

Fr

@nikthedrought

Жыл бұрын

ong

@sandhan1t1zer

Жыл бұрын

for a second i thought that it said $1000

@johnchen2325

Жыл бұрын

@@sandhan1t1zer But it's worth more than a thousand.

@abhilashasinha5186

Жыл бұрын

@@johnchen2325 sand hanitizer?

Wow I've almost obtained my bachelors degree in Aerospace Engineering and I finally get to see why the derivative of a polynomial is the way it is, thanks for your great videos and insights!!

@theguybroseph

2 жыл бұрын

This gives me hope hahaha

@tuneboyz5634

Жыл бұрын

@@theguybroseph thats great little Ben

@fernandotanase114

Жыл бұрын

Can you give updates on the searched/found jobs once you've got your diploma, please.

@jebediahkrimsoncraftleding3012

Жыл бұрын

Embarassing.

@Tech_Gamers

Жыл бұрын

Thank god ,we're all safe to fly in your airplanes now💀

I'm not sure which one I find more amazing: the math itself, how clearly you explain it, or work you put into the animation.

@sakuhoa

5 жыл бұрын

Both

@Anonimowany1

4 жыл бұрын

WIsh I had all these KZread Videos when I was still at school like 10-5 years ago. I loved math and physics. (I studied math and physics at the university afterwards) The way those subjects were taught at school was plain and super boring. All these videos on KZread are so fun and I learn even now from all these. I believe in the next decade or so - some really clever minds will arise - smarter than Einstein and Stephen Hawking and all others. Just due to the fact the way all the knowledge is provided and super easy to learn and visualize with the current age of technology. It literally wasnt like that even just a few years ago. The future is looking bright.

@deedewald1707

3 жыл бұрын

It's all amazingly awesome !

3Blue1Brown, I'm a master's degree student in theoretical physics with 1 year left, and probably not in your intended target group. Despite many of your videos covering "basic" (read: essential) topics, I find them fantastic tools for refreshing my knowledge, and even learning something new. For example, from your series on linear algebra, I learnt to visualise the columns of matrices as transformations of the respective unit basis vectors, which has been a great tool for when I have been reading group theory and quantum field theory, even though it was such a simple observation. Thank you for these videos! I look forward to more!

@ElchiKing

7 жыл бұрын

Well, I would consider myself a quite good math student and yet I can still learn much from these videos despite "knowing" most of the content already.

@Krunschy

7 жыл бұрын

+Elchi King Yeah, even though you already know through theory what the formula of the derivative and such things is, having such a great visualisation of it, really makes things easier when trying to learn and picture new you learn related to that topic.

@kylepoe5139

7 жыл бұрын

Imagine that you yourself are a graduate student in theoretical physics. You want to express your appreciation for a video, but you want to actually frame it in the context of why you appreciate it. Just saying "cool video dude" doesn't really do much. Taking the time to explain why something is useful despite not being a member of the intended target audience is far more useful to the man who makes these videos, and it is undoubtedly nice for 3blue1brown to know that his work is appreciated by people in academia as well as high school students cramming for their AP test. If someone pursuing a degree in theoretical physics cannot even state what they are doing with their life without apparently sounding like they are bragging, then it is truly a sad state our society is in.

@mikehaskel8455

7 жыл бұрын

I agree with Kyle Poe. There are plenty of people out there who, beyond being good math students, live and breathe this stuff every day as part of their profession, and really do pretty much know everything in these videos already at a deep level. After all, the author can't be the only one in the world qualified to make a video like this, can he? But these videos are still so well constructed and explained that they're worth watching for a fresh take.

@joshuapollard184

7 жыл бұрын

In one of the linear algebra videos when he said eigenvectors stay on their same span during a change of basis which means that they're just the axis of rotation, I think my jaw literally dropped

Every student who says "Math is the toughest subject" really means that their Maths teacher did NOT do a good job teaching them math. Am one of those students! This video rekindled my interest in Math as an adult. I wish this existed during my school days

@shadymello9146

Жыл бұрын

Or the ones that didn't practice enough... sincerely, A student of the latter kind

@Mr1987atul

Жыл бұрын

The people with such deep knowledge will ask heavy salaries. Bcoz they know their worth. And schools cant afford such teachers. Which is why we get poor education from teachers with poor

@MrCmon113

Жыл бұрын

Bullshit. Math IS the hardest subject, that's not the teacher's fault, but simply in the nature of the thing. You won't find a mathematician, who is not vastly above average intelligence and thinking about problems all the time.

@thewonderer9551

9 ай бұрын

@@shadymello9146Its not only about practice. If a student doesn’t understand irrespective of practice for so many times & if a teacher isn’t good enough to make the student understand, the its not the fault of that student.

@No-cg9kj

4 ай бұрын

No...most people are just really dumb when it comes to math lol.

59 years old and Grant is taking me to school. Thank you!!!

"The Essence of Combinatorics" is something I would really really love to see from you! Keep up the good work!

@pratikshayadav9279

4 жыл бұрын

Yes please please

@aniruddhasanyal7625

4 жыл бұрын

Yup

@useltrummis

4 жыл бұрын

notice the point and draw a line.... time is created from 0 to 1 too... i dont remember a nicer conciser version of "how to press start" dug deep, dude

@aarushiaiyyar

4 жыл бұрын

Yes yes yes please. Please cover vombinatorics and probability.

@High_Priest_Jonko

4 жыл бұрын

Fact: Most adults could never pass a course on Intermediate Combinatorics

It literally took me months to understand this video but I’m super glad I do now. Thank you so much 3blue1brown

I'm studying engineering 10+ years after leaving school. This series is a blessing! I never took calculus or advanced maths fomally and I could not properly grasp the concepts through the book material. Seeing this laid out in such a clear, visual and logical way is sublime. Thank you for taking the time to create such in depth videos.

@bamunua

8 ай бұрын

I definitely agree with you

omg this channel makes me think how poorly these concepts were explained in school. Keep up the good work.

@Mr1987atul

Жыл бұрын

The people with such deep knowledge will ask heavy salaries. Bcoz they know their worth. And schools cant afford such teachers. Which is why we get poor education from teachers with poor knowledge.

I have a bachelors degree in mathematics, and even though I was a straight A student, I never really "got" why we did what we did to solve problems, just that we had to do it.. until your videos. Thank you for giving me such clarity on a subject I love with all my heart and a full understanding of why problems are solved the way they are! You rock.

@cubicinfinity

4 жыл бұрын

I started watching these videos when I started learning calculus but I stopped because it conflicted with the way I was being taught. It's a better experience after having gone deeper into calculus and watching these again. I'm solid enough in it that I can keep track of the different mindsets.

@sidharths9416

3 жыл бұрын

@@cubicinfinity You are absolutely right bro. Me too had the same experience. In fact watching these after all that taught in our schools/colleges is really making us fall in love and admire these concepts

@nerd2544

3 жыл бұрын

@@carlgauss1702 How did you get a job then?

@leelaanandabhavan3083

3 жыл бұрын

Well....I think you suck.

@the.abhiram.r

3 жыл бұрын

@@sidharths9416 my teacher just gives us a bunch of formulas lol

Nice video. My University's teacher used this to intoduce us to derivatives

@Anonimowany1

4 жыл бұрын

WIsh I had all these KZread Videos when I was still at school like 10-5 years ago. I loved math and physics. (I studied math and physics at the university afterwards) The way those subjects were taught at school was plain and super boring. All these videos on KZread are so fun and I learn even now from all these. I believe in the next decade or so - some really clever minds will arise - smarter than Einstein and Stephen Hawking and all others. Just due to the fact the way all the knowledge is provided and super easy to learn and visualize with the current age of technology. It literally wasnt like that even just a few years ago. The future is looking bright.

@rohan1002

4 жыл бұрын

If I only had the same teacher.

@primeroyal7434

4 жыл бұрын

He/she should get a reward.

@primeroyal7434

4 жыл бұрын

He/she should get a reward.

@cantseeme9886

4 жыл бұрын

uhh, me tooo ahaha

I took calculus in college. The professor explained how to find the derivative of a polynomial. I didn't learn until many years later, after I graduated, what a derivative actually is.

@No-cg9kj

4 ай бұрын

Then you just didn't pay attention or read the book.

I'm 14 and love these videos-they really help me understand calculus though especially since this is a series I would say a bit more pausing and giving the viewer a chance to work it out themselves would be helpful to keep engagement, but apart from that these videos are amazing and I love this series, even six years after you released it! Thank you so much!

This reminds me my high school teacher who was really great at teaching, instead of force feeding us formulas to remember, she would first show the proof of why it is what it is. The first time I saw a mathematical proof it was mind blowing. Unfortunately not many math teachers actually even know proofs, and most kids around the world are getting gavaged with rote memorization of terminologies and formulas they don't understand... :(

@evanchong6482

Жыл бұрын

tbh not everyone needs the proof, alot of us just studied maths to pass and we really couldnt be bothered to learn the history and context

@RenatoKestener

Жыл бұрын

@@evanchong6482 that is exactly the point. "Studying to pass" makes no sense. It is the same as saying "living to die". Study should be about proof, about curiosity, about exploration. This is what makes humans a miracle and not slaves of some nonsense way of living...

I know it’s a bit late, but may I just say that this is an absolutely phenomenal series. It really helped me understand calculus in a way that just didn’t happen at school.

@redpill6379

3 жыл бұрын

At school they teach u for exams that's why.

I love that even though I've been an avid student of math for most of my life, preaching its wonderful usefulness to anyone who will listen, your videos will invariably contain 50% of things I have learned, and the other 50% wisdom that is gained only by tying all fields of math together to produce a bird's eye view of a master concept. That extra amount on top of the base material represents you trying as eloquently as is humanly possible to share your bird's eye view with the world. We are fortunate to have your passion and knowledge used in this way, and we can only say "thank you!"

As changing my career from a Data Analyst to a Data Scientist, this video really helps me to brush up my calculus to learn advanced statistic models. It changes my future, thank you for interesting and awesome video !

I'm a french engineering student, and despite the fact that I already know these things, I love watching your videos because your way of talking about maths and illustrating them really makes me wonder deeper questions than what I already learnt. Great job I love your channel 🙃

@ChiChiStrawberry

7 жыл бұрын

Evi1M4chine This probably sounded a lot more passive-aggressive in my mind than I think you intended it to? I would say that engineering students do understand things deeply, but there will always be people, in any field, that simply accept rules and move on. But again, that's only a few people, not all people. Videos from this channel are made for the purpose of curbing that, however, and that's lovely! :)

@zeronothinghere9334

7 жыл бұрын

Paragraphs please. My eyes hurt. E: On the other hand we've got to ask this: Should education teach them how to live, or should it teach them how to think?

@Fyizze034

7 жыл бұрын

Evi1M4chine I 100% agree with Yue Chi K, I think in any field there will always be people trying to cheat as you said it properly, but they won't be good engineer, surgeon, teacher, etc... According to me, some professions require passion or at least interest to be able to work in correctely, and engineer is one of them, I hope your flatmate won't realise it too late.

@vampyricon7026

7 жыл бұрын

+

I think it's safe to say that by impacting millions of people watching your videos, you've single handedly made the world a little bit better place.

This is great! I used to study maths at school in such a bad way, through memorization and solving problems in an "automatic" way, without studying the actual reason and meaning of mathematics. Now I'm at university, reviewing again some fundamental topics and I'm seeing maths in a completely different way. Your videos are great and are helping me a lot to discover new things. Keep up the great work! Ps: Sorry for some grammar mistakes, I'm learning English.

I have no doubt that this is one of the most clearest and satisfying fundamental math topics videos available in the planet. What an amazing useful and enriched piece of content. Thank you so much Grant, now I have totally understood this concept on a intuitive way

I like the black background. Bc i see how stupid my face looks when I'm watching those kind of videos 😅

@dunkeykung1162

4 жыл бұрын

It's a whole army of stupids then mate, onward my fellow viewers!

@jasperlee2238

3 жыл бұрын

lmao

@bananachocolatepistachio8696

3 жыл бұрын

This is why I dislike the black background

@realbignoob1886

3 жыл бұрын

lol

@salahshayah9864

3 жыл бұрын

Best comment

I “learned” derivatives at school today. My teacher said to write down the definition on the board but not the crossed out portion which read “it’s almost like finding the slope at a single point.” And then he gave us this formula, f’(x)=lim(h->0) (f(x+h)-f(x))/h. I spent the example problem time as time to figure out how this equation gets the derivative. Thank you for showing what derivatives are and not a random equation that means nothing to most people.

@jorriffhdhtrsegg

Жыл бұрын

At least you remember it. I am sure we had a 'slope of line on curve' lesson and think "um ok why, just playing around with tangents now?". Well its only the foundation of classical physics, involves infinite limits and all sorts, but anyway...if only i knew at the time instead of "No JuSt LeArN iT"

This is brilliant - I have struggled with calculus and at the age of 61, this has made it so clear! Today's students have some tremendous resources available to them.

I am 13 years old and I Would like to say thank you for this incredible series it has helped me a lot in my Studies of mathematics

@kv-2450

Жыл бұрын

Mf is 13 and doing calculus

@wellyesbutno9396

Жыл бұрын

ok

@25nacesanleedaltrez58

11 ай бұрын

keep it up!

@rabia1180

8 ай бұрын

beautiful! lots more cool stuff to unlock :)

Here I am, Professor, taking notes as if my life depended on it...Thank you very much for an excellent, much expected and very illuminating series!

Being an undergrad student, studying at a level a little more advanced than this, your videos really make me take a step back and appreciate the beauty, a sort of 'stop and smell the roses' for math. Thank you, 3Blue1Brown for being a brilliant educator.

@xanderlewis

5 жыл бұрын

Same here. I first watched this video when it was published almost exactly two years ago, and coming back to it now is something really beautiful. At the time, whilst I could follow it and gain a lot of intuition, it seemed quite complicated and it was difficult to really see how it fit into the ‘bigger picture’ of mathematics. Now I’ve nearly finished my first year of undergraduate mathematics and been introduced to the more general principles and some of the more rigorous constructions of calculus, this is just wonderful to see again. It’s encouraging to see how much progress I’ve made personally in my understanding but also to see how almost exactly the same techniques used in this series can be applied in so many ways to obtain all sorts of other incredibly beautiful results in other areas. The fact that much of mathematics is so ‘useful in the real world’ seems like a wonderful coincidence, because even if it wasn’t... it’s just so....... lovely. ♡

These videos are super good, this feels like something that I would have to pay for on an online course. I originally had no interest in calculus, but now I love it since you're always able to explain it with real world examples that are easy to visualize and understand. These make me really look forward to when I take calculus next year!

Damn this is amazing. I have a calc test in a few days and I don't wanna rush any of this. It's to beautiful and I watch each episode like 5 times to really grasp the idea. I usually shrug at patreon but once i get my pay check i have to support. Thank you so much for helping me understand, but mainly, helping me appreciate math so much more.

In college my Calc 1 professor led us to the point where we could see the derivative for ourselves. When, in a homework assignment, I did just that, he implied that I must have taken calc in high school and been pretending to have had that breakthrough for myself. A real kick in the jibblets. Some people just shouldn't teach. When I read your intent for this video series, it really hit home! Thanks for allowing folks to experience the wonder of discovery.

10 days of Calculus videos, 10 days till the AP Calculus Exam. Coincidence? I think not!

@nestorv7627

7 жыл бұрын

lmao, I'm just waiting for him to explain deeper Euler and Newton's method, and the Lagrangian Error Bound.

@SpaghettiToaster

7 жыл бұрын

newston's method is not an essence of calculus

@williamshearer5506

6 жыл бұрын

Erik Beserra no

@SimonS44

6 жыл бұрын

yo soy arból 5 lol is the second-worst grade here

@eldesconocido5992

6 жыл бұрын

Erik Beserra .

Thank you so much for this. Your explanation makes so much more sense than "decrement by one and multiply by the old power". It's far better than just regurgitating what teachers say.

I love this series! I am currently taking AP calc in high school, and this is the most sensical explanation of derivatives i've ever seen!

OH MAN, THIS IS GONNA BE GOOD

@bumdeedum8771

7 жыл бұрын

Ethan Rojek You be right mate!

@Aequorin628

7 жыл бұрын

HELL YEAH! LET'S DO SOME CALCULUS!

@umnikos

7 жыл бұрын

Ethan Rojek I CAN'T WAIT UNTIL I BEGIN SOLVING THE 3x+1 PROBLEM USING CALCULUS!!

@breckr1121

7 жыл бұрын

Evan Bialo AWW FUCK YEAH CALCULUS

@joraldthewizard2327

7 жыл бұрын

kkk

We are truly honoured and privileged to have access to the thought processes of the giants who have gone before.

@ThinkTank255

6 жыл бұрын

"Sometimes when everyone is standing on shoulders of giants, it is better to be an ant." - ThinkTank255 What this means is that it is great to make progress based on the works of others, but sometimes, we must challenge and question even the giants to make progress. Remember, these giants were humans, just like you and I. The idea that we cannot improve on the foundations of mathematics itself should never be assumed simply out of honor or veneration of the great men that came before us. Indeed, I think many of them would themselves be honored to be challenged and even proven wrong. I think mathematics has, to some extent, lost its way. It has been standing on the shoulders of giants for so long, nobody knows how to be an ant. There is a lack of critical thinking, even within mathematics itself, which is actually quite frightening. To put it metaphorically, standing on the shoulders of giants leads one to believe that maybe the giants shoulders are the only way to elevate oneself and maybe no mathematics exists where giants don't exist. In contrast, I think mathematics exists everywhere, and we can invent new mathematics and new ways of doing things if we try hard enough. We need not be bound to the dogmatism that exists in mathematics.

@asemhisham3507

5 жыл бұрын

Well actually... Human brains evolve over time... Meaning most of us are smarter than newton and the others.... But we are a light year behind their determination... Many of us are just too lazy and thats true and its a fact

@adeelali8417

5 жыл бұрын

@@ThinkTank255 It's not convenient for a person to do this though. You're right though there may be other crazy math that we will never find.

He makes magic using just a bunch of living pi symbols with eyes and some really good graphical animation. Hats off. Never going to forget how you helped my in my quest of ultimate knowledge. Thank you. Makes me question what schools even do.

@sir_albaxious1909

4 ай бұрын

Relatable with me. I wanted to learn calculus because it just passed through my mind one day. I thought I would learn this after a some years and that learning it is impossible. But as I begin learning, I realised that this branch is the most beautiful branch in all of mathematics. And yeah, I learned this for the purpose to use Integrals in my work and for ultimate knowledge.

Man, I am so grateful and thankful for your explanations. I've never felt enjoyment of learning something in last 4-5 years like this.

LOL physics students be mad speed and velocity thrown around everywhere

@nucle4rpenguins534

5 жыл бұрын

I actually enjoy velocity problems lol

@katienewman4743

5 жыл бұрын

And the use of distance and not displacement, but this is an amazing video (and channel) lots of love!!!

@henryg.8762

5 жыл бұрын

yas

@saiavinash7432

5 жыл бұрын

@@katienewman4743 them vectors are a bitch.

@chucksucks8640

5 жыл бұрын

speed is the magnitude and velocity is the direction with magnitude.

"when you bind yourself to all but just a single instant, then there's not really any room for change." true in math and in politics.

@MrOdsplut

4 жыл бұрын

Sameen Dusk We live in a society.

@mannyheffley9551

4 жыл бұрын

Are those any different? hMmmmmMMmm

@squibble311

3 жыл бұрын

ew politics

@calebjohn6159

3 жыл бұрын

@@MrOdsplut we live in a society

Absolutely fascinating the way for you to explain these concepts. If I just had been explained this way, I would for sure be a genius creating ultra mechanical devices very helpful to the people. Now is way to late but the fascinations persists. Thank you for this outstanding work.

Math has never been this exciting to me !!! I'm so grateful that channel like this does exist on youtube Love from Vietnam

Your work here has permanently changed the way I think and how I feel about Mathematics and life in general. Please keep up the good work. When you feel down, please remember that there are so many of us that are grateful of what you have done here.

Next up with be "Derivative formulas through geometry". Keep track of the full playlist at 3b1b.co/calculus If you are curious, as some commenters have pointed out the way an actual car's speedometer works is to induce a current with a magnet whose rotation is determined by the rotation of the wheels. Depending on your view of the underlying reality behind certain physical laws, some might call this a genuine "instantaneous rate of change", but it still leaves the question of what exactly that phrase means. As far as setting the stage for learning calculus, and inventing the math needed to capture this concept, I do think it's important to recognize that the idea of a "change" makes no sense when you blind yourself to all but an instant. This is why the derivative of a function, which extends the idea of a rate of change to make sense for a single instant, is intimately tied to the function's value around that point. Perhaps there is a statement to be made about how physical laws determining the state of a system at a given time are intimately tied with the surrounding points in time, but that is beyond the scope of the series.

@amo6139

7 жыл бұрын

great video

@raymondsutrisno9032

7 жыл бұрын

There is a mistake in the notation at 13:30, shouldnt it be ds/dt of s(t) not ds/dt t. or d/dt (s) or d/dt of t^3

@Quacky_Batak

7 жыл бұрын

At, 9:13, how come you calculated the derivative at t=10, isnt the graph discontinous?, also, by your intuition(which is best), we can't extend ds "just" above t=10. BTW great video love ur stuffs!!

@zairaner1489

7 жыл бұрын

The graph isn't discontinous at t=10, we just looked the function in the intervall (0,10) and it isn't even clear wether 10 is in the intervall or not. You can define the derivative even if the intervall is closed, in which case you just have the limit from one side in the boundary points

@zairaner1489

7 жыл бұрын

dt is not a number! Thus it makes no sense to say its zero, and also no sense to subtract soemthing from it. It's just notation for the limit

0:00 intro 1:07 central example 2:20 velocity 3:26 change in time 4:32 ds/dt in the real world 7:13 tackling the paradox in pure math 9:44 the true derivative 13:11 take a step back 14:18 "instantaneous rate of change" 16:23 outtro

I am in love with this method of teaching and the mathematics visualization program you created, Manim, is amazing! I am going back to school to learn Computer Science and I am excited to know that soon, I can begin utilizing Manim as well! Thank you for everything you do.

Your animation bringing the secant line down to a tangent line really drove it home. Thank you so much.

Anyone can be intelligent, but only those who can successfully articulate their incredibly intelligent ideas are brilliant. Great video 👏

@uzairakram899

4 жыл бұрын

ese est percepì

@AthAthanasius

4 жыл бұрын

"If you can't clearly, and succinctly, excplain a concept to someone else, then you don't truly understand it yourself." - Paraphrasing 'someone'.

@montanasnack7483

4 жыл бұрын

@@AthAthanasius Thats exactly what i wanted to write

@daywill8849

4 жыл бұрын

@@AthAthanasius Richard Feynman

@fahdal-sebaey3322

3 жыл бұрын

@Emma Wood .. Do you mind if I steal this quote for my book, desktop, discussions.. and pretty much everything?

It is astounding how much better of a teacher you are than my calc professor. Thank you for taking the time to make these videos, the level of intuition I have received from this series has been incredibly helpful. Maths are taught like shit in universities - I know this because watching your videos for an hour has given me a more in depth understanding of these concepts than my entire semester of calc 1. You sir are a legend. Anyone who is struggling with calculus should stop what they are doing and watch this series in full.

This is incredibly good teaching. Even after 4 years of an engineering degree I still found myself relying on the higher-level rules of calculus without paying enough attention to where the rules came from. This has finally sewn together my learning in a way that will stick in my mind. Thank you.

One thing...Please don't stop making this kind of videos🙏

The choice of colours for “instantaneous” and “change” was really clever. I love your attention to detail. Thank you so much!

man if there is a heaven I am sure you will go up there. I am forever grateful to you for building this concepts with in me. I think a thank you would be small but from the bottom of my heart thank you, you are great. supporting you on patreon is my one of the bucket list once I get a job.

THE 👏🏻 FACT 👏🏻 THAT 👏🏻 THESE 👏🏻 VIDEOS 👏🏻 HAVE 👏🏻 NO 👏🏻 ADS👏🏻

Being a mathematician working on the financial industry (and despite what you might have heard about financial markets using maths quite often and rigorously) who wants to recover part of my former mathematical reasoning and intuitions lost among nonsense, nonrigorous and nonscientific economic pseudo reasoning, I couldn't have stumbled upon a better resource than this channel. I will only say congratulations, because no matter which words I pick, they will do no justice to the art performed here. As announced, congrats!

Thank you so much for calling out the "instantaneous rate of change" oxymoron. I pointed it out in to someone and they overruled my point simply because they pass exams better than me

"It´s kind of FLIRTING WITH THE paradox of change in an instant whithout ever needing to actually TOUCH IT " 3Blue1Brown That was funny :D

These are bar-none the best math videos I have ever seen. Thank you, Grant! You are a national treasure.

my mind was literally blown when he explained how you can just... ignore terms containing dt so intuitive!

@lukaszspychaj9210

3 жыл бұрын

I had to stop the video at that moment. Wow

@Brahvim

3 жыл бұрын

Same! (I realized how you can always break down a fraction later)

Fun fact: The reason the displacement function is denoted by s(t) goes back to the German word for distance, "strecke" (despite the fact that this is the word for distance and not displacement).

@LaureanoLuna

5 жыл бұрын

Are you sure it doesn't come from the Latin Word "spatium"?

I just would like to say thank you so much, I have watched these over and over and each time I feel like I understand a little better... It makes it so much easier when you REALLY understand it.

I am incredibly thankful for this series. It's hard to find teachers that teach at such a level that cares for true understanding

The amount of times I went like 'oh' and 'aha' and 'wow' says clearly about how much of an enlightening experience this was. Thank you so much!

When I learned calculus, for t>>0 instead of d(t) we used Δ(t). This notation was helpful for me to understand the concepts you discuss so well.

@miholju

4 жыл бұрын

"Sleeve of Wizzard" - Borat

@vincentstone7272

2 жыл бұрын

My calculus teacher teaches us that the reason we use "d" intstead of (delta) is because d is latin script and delta is greek script... don't know if thats helpful

@19divide53

2 жыл бұрын

@@vincentstone7272 Except in mathematics, except for the conventional ones (e, π, special functions, etc.) you could use any of the Greek scripts or Latin scripts as symbols for mathematical objects. It's perfectly valid to write τ^2-τ-1=0 or "let Λ be a connected open set" or "Θ(x,y)=χ(x)ζ(y)".

@quinntolchin3080

2 жыл бұрын

@@vincentstone7272 @nomi udo Δ(t), represents "a defined change in t", whereas d(t) represents "a change in t that approaches 0". Grant used d(t) as if it was Δ(t) in this video for informational purposes, but really saying that d(t) ---> 0, is redundant because that is what the "d" represents. Whereas the "Δ" just represents a change that does not necessarily go to 0 unless you take the limit of it. In other words d(t) is a shorthand notation for the limit as Δ(t) approaches 0.

He has truly achieved his initial goal of the series. I do feel what those mathematicians would have felt just after discovering derivatives and the unique formulas for a few of them. Congratulations. Hats off.

WOW! Fantastic explanation. I've been trying to understand how to calculate derivatives since I took Calculus in business school 30 years ago, and you just clarified it all for me. Wonderful job! Thank you!

As a precal student, your videos actually hype me for calculus next year. I love to be ahead and have a clear understanding of calculus going into school next year.

@terner1234

5 жыл бұрын

@@DoesMahBlockLookBig what didi you learn in school until this point, did you get to integrals?

@DoesMahBlockLookBig

5 жыл бұрын

star of duty Just yesterday we touched up on the basic definition of a definite and indefinite integral. Right now we’re taking baby steps by using Riemann Sums and Trapezoidal Rule to help us visualize how integration works.

@terner1234

5 жыл бұрын

@@DoesMahBlockLookBig since english isn't my first language, I don't completely understand what you're talking about. I don't think we even learned what integrals are except for "the opposite of derivatives" or "the area between two graphs"

@Ashebrethafe

5 жыл бұрын

@@terner1234 Riemann sums are what was discussed in the first video -- an approximation of the area under a graph as a sum of the areas of rectangles, calculated by (a) splitting the part of the graph for which you're measuring the area into several pieces; (b) choosing a point on each piece of the graph; and (c) calculating what the area would be if each piece were replaced by a horizontal line passing through the chosen point. (If I recall correctly, the actual definition of an integral is the value that the Riemann sum approaches as the width of the widest piece approaches zero.) The trapezoidal rule is a similar idea, but with trapezoids instead of rectangles -- instead of replacing each piece with a horizontal line through a single point on that piece, you replace it with a straight line connecting the endpoints of the piece.

@alexovichsky

4 жыл бұрын

Then you will be that annoying know-it-all student who sits in the front and tries to lecture the professor.

SOOOOOO glad I found your videos. I am a science teacher, and my math has gotten rusty over the years, so I am trying to dust it off improve. You are bringing so much clarity to intuitively difficult concepts. Thank you!

Thank you. I am reaquainting myself with the basics of Calculus in a Calc 1 class. I took courses in high school nearly 2 decades ago and had senioritis the entire year. I love your reasoning and your intuitive problem solving methods. I will recommending your channel for further conceptual development for any of my classmates.

I am in pre-calc right now, and this is soooo helpful! Thank you

Even though this video explains a concept in an amazingly beautiful way I still have to watch it multiple times to even kind of understand what he’s talking about

The way you present the information in such an organized and compelling way is incredible

This method of explaining calculus really just makes sense, it's so elegant and simple yet still tackles the core elements of what calculus is, it has really helped me learn

Thank you so much for making these videos. They explain everything so clearly and calmly while still preserving the beauty of the mathematics. I'm in middle school, and even I can understand the ideas presented in this. This has been very helpful.

I've always wondered whether it's possible to do an absolute perfect and flawless math instructional video. After watching this one, I know it is.

This is the kind of tutorial that makes me love mathematics. Congratulations for the great video

I am studying a masters in meteorology and your video has just blown my mind! I am so used to integrals and areas under curves etc etc and have NEVER thought about the fact that calculating a velocity, or acceleration for that matter, at a single point in time is the most bizarre thing when it is measuring a change. Amazing.

I've almost burst into tears during watching this. The derivatives have never been so clear to me. Thank you so much, exactly what I've been looking for!

@mauriziop4307

Жыл бұрын

since is so clear for you maybe you can help me .sorry for my stupid question .in this video the derivate is 12 ..but 12 what meter for second ?it should be the istantaneous speed and so how is possible it s the same at any point?thanks in advance

@fehgmenshcr2427

5 ай бұрын

​​@@mauriziop4307The slope of the tangent line to the graph is 12, he just ignored all the terms with dt in them because dt is approaching 0, so it's a REALLY small number, but not 0 and not infinitely small too. So those were safe to ignore

I've never been so excited for a video series! :o

@symbioticcoherence8435

7 жыл бұрын

I have... for the last video series of 3Blue1Brown :)

The music + Grant’s voice + the visuals + the content make this channel my favorite math KZread channel.

You are a genius! If I watched your videos 30 years ago ( when after my math course I have no idea what a derivative and an integral were all about ) I would have been less intimidated and would have considered to become an engineer what I was sure not be able to become

This is awesome so far! I've learned this stuff in calculus but I'm starting to have a much better understanding looking at it from this perspective!

6 minutes in and I've already learned more about rates of change than in my high school and college calculus classes combined

I'm studying for my master's degree in theoretical chemistry and I love watching these videos. The "Essence of linear algebra" helped me to understand change of basis and linear transformations like no other video could. Thank you so much and keep up the hard work.

@TruthBeTold.

5 жыл бұрын

same for me tbh

hey usually i don't comment on any video but the insight and thought process it developed in me, made me realize that this really worth it. This video develops firm root in calculus. Really thankful to you !!

amazing this is helping me a lot with understanding the fundamentals of calculus, i think anyone who is struggling, with calculus needs this.

If we are keep looking for what we want, someday, we see it. After years, this channel hits me with WOW.

thank you patreon,you just made me see the useful part of furthermaths,even though i live in Nigeria

I appreciate this soothing background music, it's so calm and peaceful to focus.

12:22 this was the moment that made it all click. the factoring, and then treating the dt terms as 0 (since the limit of dt is 0). Once laid out, it looked so simply, yet so brilliant. I wish I had seen this video sooner. Thank you 3b1b