## 48 thoughts on “What they won't teach you in calculus”

1. 3Blue1Brown says:

Instead of the follow-on I originally had in mind, which would extend these ideas to complex functions, the next video is on Divergence and Curl, as part 1 of 2 for an interesting application of complex functions with derivatives: Take a look! https://youtu.be/rB83DpBJQsE

2. PagezMusic says:

i just realized this guy sounds like dave rubin and now i cant unhear it

3. Threelly AI says:

4. Jerrod Shack says:

With the combined knowledge of calculus class and this video, I know everything there is to know

5. Tyler White says:

This video should contain the meaning of life

6. Zaralho DZN says:

Dude I barely know what they DO teach me in calculus, let alone what the don't teach me.

7. Memetastic Bot says:

8th grade me trying to understand what hes saying

8. Statici says:

I jumped into the "advanced topics in math" class at my college a couple years ago…it was about discrete dynamical systems; a topic that the professor's PhD thesis was centered around. Without a single doubt, despite struggling with the class because I had to get an exception for my lack of a proofs class before taking the highest-numbered math class available, it was my favorite math class ever. By FAR. It lent to me an understanding of not just how calculus works, but also how it was derived, and how it connects to physics (my major). It is rarely mentioned (probably a product of how it is not often offered to undergrads) but it's just…cool as hell. Thanks for doing a video on it 🙂

9. derlil says:

confused as fuk

10. Happy Shawol says:

11. Daniel Mendoza says:

I’m barely learning Trig why am I watching this

When he said the derivative of phi was .38, I expected the derivative of 1/phi to be -.62, but it was -2.62 – I wonder how these derivates and -3 are related

13. kumar anurag says:

I took brilliant from your code, just to show you my support, nice video man

14. Mou Lin says:

Differential as an operator: where linear algebra and calculus meet!

15. WhimsyHeath says:

I still feel like I don't fully understand how to find what the density of the derivitive at a local area is, but still, really interesting video! Doesn't help that I don't learn maths in education anymore, but I do enjoy the ideas when I don't have to drill all the exercises!

question, though, you say how it's like a circle but slanted, that makes me wonder, what happens when you get the golden ration – 1? ie. just 0.618 or whatever? is there any special property of that? it seems like it should if it's a fixed point of the standard 1/x. especially because circles are interesting.

Also, where can I learn about the golden ratio? it's a weird number that pops up in the weirdest places, like it being the most irrational number, and stuff.

16. MrGregorychant says:

YouTube, why are you recommending this to me? I still use my fingers to add numbers.

17. Eric Peterson says:

What they won't teach you in calculus is: it is a pointless class for anyone but engineers, math majors, and physics majors. Stop teaching it as a required class for anyone that won't need it.

18. Tom Williams says:

Can someone explain why X=3 changes by a factor of 6? We're looking at x^2, right? Shouldn't it change by a factor of 9? 3^2

19. that random pieceof gum I I found on the street says:

Damn it. I thought this was gonna be math titties

20. Keet Randling says:

Sorry, wrong: What they don't teach you in calculus, or trigonometry for that matter, is: WHAT THE BLEEP DO YOU USE IT FOR?!?!

I dropped into AP trig mid-semester, and took calc the next year – passed both with very good grades, AND NEVER HAD A CLUE WHAT TO DO WITH ANY OF IT!!

So easy to do the calculations, that's all algebra – but WHY WOULD I WANT TO KNOW WHAT NUMBER A DERIVATIVE IS BEFORE I KNOW WHAT A DERIVATIVE IS?

Really! These subjects should be taught as more than just boring mathematical puzzles, but as real-world applications.

21. Will T says:

You can actually use the arrows drawn at 10:25 to visually see both 1) where the fixed points are and 2) which one will be stable. It’s pretty easy to see that every arrow is tangent to the curve in the middle.
1) This means that the points where the tangent is vertical will correspond to the fixed points, which are, after all, just the places which go straight down without going left or right.
2) Once you have found those points, look at the curve again and note the vertical positions along the curve of the places with vertical tangents. The one on the left is above the midpoint between the two number lines, while the one on the right is below the midpoint. This means that around the one on the right, the arrows do the majority of their horizontal movement before touching the curve (and the vertical arrow aka fixed point), while on the left, the arrows touch the curve (and therefore the fixed point) before the middle of their horizontal motion.

22. Rengar says:

i didn't understand

23. TwinPotatoes says:

You lost me at the negative slope transformation visualisation… 🙁

24. Zeglo vrk says:

Is this kinda like the Jacobin matrix det(A) warp?

25. Maya Balaji says:

26. Chris Frank says:

Thank you for all of your videos, they really do provide a much deeper understanding of the topics. Also, thank you for directing me to brilliant.org, it really does have a lot of useful courses.

27. gnorf norf says:

ok real talk rn the amount of views is 1.618 mil this is some scary coincidence stuff

28. Hattori Kanzo says:

Actually, my coaching classes taught this, 😁

29. Mehardeep Singh Bhalla says:

Loved!

30. alan makoso says:

At 7:15 did you realize the quotients are the Fibonacci sequence's quotient.
1/1=1
2/1=2
3/2=1.5
5/3=1.6667
and it approaches phi. In the video, 3b1b replaced the divisor with the previous output, took the inverse, added 1 and it still worked just with different values. So Fibonacci isn't the only way to approximate phi, any number can, you just have to do it right. To see it for yourself copy and paste the following code into any java complier.

import java.lang.Math;
public class Main{

public static void main(String []args){

System.out.println("Made by Alan Makoso"); //the most important line of code

double divisor;

double initial = (int)((Math.random()*150)+1);

System.out.println("initial value: " + initial + "n");

int r=0;
while (r<80) {
divisor = 1.0+(1.0/initial);
initial= divisor;
r++;
System.out.println(divisor);
}
}
}

31. Takeo Fukumura says:

What they won't teach you in Calculus:
US History

32. samin yeasar says:

Well , I need some mathematical software where I can calculate calculus easily and can analysis graph In short time . I want to input some equation for output through graph . So It would b very helpful for me if u leave some links to me about thos software.

33. Actuaría Cuarto Semestre says:

I finished seeing it and understood very little.
Around 4th or 5th time finally understood the whole idea. I don't know how to feel about it:/

34. willem schipper says:

Wow this is pretty cool

35. willem schipper says:

10 things your calculus teachers don't want you to know

36. Qermaq says:

The Merriam-Webster app pronounces then “pye” and “fye”. Good enough for me, but if you choose to say “fee” then you must also use “pee” or you’re a hypocrite 😉

Too much illustration kill the illustration. Things is redandant among other utubes. Be more precise and less self philosiohical thoughts

38. Dhananjay Deshmukh says:

I almost ended up learning entire calculate in first 5 minutes if introduction

39. Neutronized says:

What match teachers don’t want you to know

40. Philip Hanhurst says:

Instructions unclear, haven’t taken calculus yet.

41. ling yan says:

You must flex those conceptual muscles

42. A VERY horny Mr.Dinosaur says:

What they won't teach you in calculus: is Calculus.

43. Samu Sammale says:

I have not even started calculus courses i dont think i should be here yet

44. Reidar Wasenius says:

Beautiful!!!! Nowadays, I always give a thumbs up right away at the beginning of each video. I have never regretted it. 🙂

45. John Chessant says:

12:02 In LaTeX, you can write |{-2.62}| to avoid that awkward space between the minus sign and the number 2.62.

46. Sheldon Robertson says:

phi's little brother is anti-phi. It is the only possible input value that when used as the starting value for the repeted function doesn't eventually become phi.

47. العم سامي says:

Awesome