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Excellent!

very thorough nice video!

Does the 4 belong there ? Don't believe so

Super explanation goosebumps tq

I really appreciate your effort

God bless you

Excellent delivery. Well articulated.

mindblown

what happens to 30 of the cars each hour?

Brilliant

cool

On the Definition, how does the differential equation apply the curve without any approval?

Great video, thanks!

You are an excellent teacher

Sorry, but there is a mistake at 4:30, X1+X2 = 255+400 = 655, and with this value (655) the system has no solution.

You do not cater for differences in speeds. I would love to see how close it is to real life though! Great video, thank you

Continue this series please

Beautiful how analogous this is to KCL

why you using delta? instead of sigma??

Need measure ultrasound force to see background biased

wow, this was very easy to understand, thank you!

e is actually a function, e(x), with the numerical value of the number e computed at x=1.

Hello. This is a nice video, thanks for sharing. I have however a comment about the proof that the two e definitions are the same (which of course they are!). At 15:30, one cannot just say that the limit of the sum is the sum of the limits, because the sum contains a *variable* number of terms, which itself depends on n. Let me make a different example. Suppose we have to compute the limit, for n → +∞, of the sum (1/n + 1/n + 1/n + ··· 1/n), which contains n identical terms 1/n. Of course the sum of the n terms is n·1/n = 1 for every n, and so the limit is 1. But if I were to take the sum of the limits, I would get 0 + 0 + ··· = 0, which is wrong. Now, in this case, the trick works, and of course the equality lim (1+1/n)ⁿ = ∑1/n! is correct, but the proof does not justify the exchange of the limit with the summation. A possible way of doing this is resorting to Tannery's theorem (which is the "series" version of the dominated convergence theorem for exchanging limits with integrals).

Such an awesome video!

Excellent 🔥 we need more sequence and series with infinity concepts, also integration

My favourite derivation of the volume of a sphere until now. This video is very intuitive and passionately explained. Thank you

Is this related to elliptic curves??

Well, judging from your thumbnail it looks like you're sliding the sphere along x and doing the integral that way. It's much, MUCH simpler and more intuitive to do it integrated over spherical shells, from the center out to the radius. It's just integral from 0 to R of the surface area - 4*pi*r^2*dr.

What is the best way to make a solid sphere using a 3D Laser Printer?

you should explain how the formula of dy/dx comes about. It is straightforward but a layman has no clue. You can talk, e.g. about the amount of change in the size of two consecutive surfaces underneath the curve. So you get the difference between (X1-m).(Y1-0) and (X2-m).(Y2-0). Any kid can understand that.

How did you get the left hand side of the differental equation? How did you know it was of first degree ? Did you just guessed ?

Accepting Hubble's finding that space is expanding and hence, our universe has a spatio-temporal origin and boundary, is apparently the conventional world-view in empirically focused natural and sub-space social science, excluding any contingent statement of form, "this may happen", since it's temporal domain doesn't coincide with this, but you may be able to 'have your cake and eat it', through dedicated notation like < as the opposite of >, instead of concatenated non-number-numeral - < number-numeral say, because the law of non-contradiction : nothing is it's opposite, is irrelevant in an instrumentalism consistent predicted world.

In video 15:05 there should be 1/2. (-1/2) appear only after integration of exponential (-u).

This was awesome!

There are over 100 such geometric proofs, I remember that Mathologe made a video about it. Your proof is a different one. I still feel that you jumped a little too far, I think you should have pointed out that the side of the smaller square is a, and the side of the larger square, b, and the side of the big square is a+b, and thus, not only does it *look* like it fits, but mathematically it fits exactly, too.

the symbol you are using for sigma is actually delta 😂

Galton board is based on Binomial theorem extraction of coefficients in you case C=(1+x)^13 expand. It has bell curve shape but Gaussian normal distribution is integral over real numbers lie. Dices, coin flips, Galton board pegs can be got also from Pascal triangle are integer numbers and has nothing to do with Gaussian norm. dist. formula.

This was really amazing

Sine is dual to cosine or dual sine -- the word co means mutual and implies duality! Summing (integration, syntropy) is dual to differences (differentiation, entropy). "Always two there are" -- Yoda. Syntropy is dual to increasing entropy -- the 4th law of thermodynamics! Duality a symmetry is being conserved -- the duality of Norther's theorem.

Bruh, I mean, good video, it was awesome, but didn’t you INTEGRATE the Superficial area of the sphere, instead of getting the DERIVATIVE of the sphere?

Always amazes me how I can understand derivations like these as soon as I look at them (I just skipped to the end and looked at the math and diagram) but idk if I’d have ever solved this on my own. I tried and all I realized was I couldn’t just integrate with discs without doing something clever before I went back to doing normal classwork. Don’t know if I’d have ever reasoned out this diagram with the right triangle. So ingenious to just integrate from 0 to r, and express each radius y in terms of r and x so that r can just be subbed for x, thereby giving a working formula.

This is a quite comprehensive video overall, but I do think it lacks a mention of /why/ that definition of normally distributed data appropriately describes the behavior of the balls-and-pegs simulation.

Wonderfull concept ! Using distance formula to prove Cosine(sum n difference of angles)! So easy to digest n remember! ❤❤❤

Awesome video! Thanks for the information, insanely interesting!

@ 14:38 Why is it -1/2, it should be +1/2 surely?

first comment This is an actually good video How did you make it? Did you use Powerpoint?

I am not convinced by the step where you integrate at the separation of variables step and you say that (x-mu) should go to (1/2)(x-mu)^2. Applying the power rule would not give that result since mu is just a constant term, where did the mu squared come from out of thin air?

Subscribed!😊

Thanks

16:06 Why isn’t is negativ e to the negativ u, instead of just e to the negativ u? When you differentiate e^-x you don’t get e^-x you will get -e^-x