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

  1. 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. Hmm… https://chrome.google.com/webstore/detail/threelly-ai-for-youtube/dfohlnjmjiipcppekkbhbabjbnikkibo

  3. 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 🙂

  4. 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

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. Your videos are absolutely beautiful and provide different ways of thinking about mathematics. Please post more!

  11. 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.

  12. 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);
    }
    }
    }

  13. 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.

  14. 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:/

  15. 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 😉

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

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

  18. 12:02 In LaTeX, you can write |{-2.62}| to avoid that awkward space between the minus sign and the number 2.62.

  19. 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.

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