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2.718

I’m sorry, but I’ve taught this for almost 15 years, and even I didn’t have a clue what was going on or where we were going.

Very good!, Probably having a polarizer for the camera would be good investment.

Great video

THE SCREEN IS TOOO BRIGHTTTT

Or just dilute the acid by 1/10,000 and run a chloride analysis bingo exact Normality or Molarity for you younger people. Same for all mineral acids, I used to standardize my sulfuric to .0200N this way also.

Can you take a look at Karl Friston’s Free Energy & Active inference.

Hey man your videos are great I'm starting to understand something , just wanted to tell you in 2:03 the Subtitle says "two girls" instead of integral

Can u make a video for the surface integral 😇😇 , Great work btw

Great - Easy for a non-mathematically-inclined listener to follow

Odd how pi popped up and brought his buddy, .Cal Culus

You did not need to grade this in HDR, but I’m glad you dud

Thanks brother, for explaining concepts in simple words, please keep uploading more videos on Multivariable Calculus

How much you seem Iranian 🤔

informative video, thank you. can you recommend a chemical that will dissolve the gasoline varnish / gum out of an antique cars gas than that has sat for 25 years with fuel in it that wont eat the steel tank?

can you go over the simplified version of Schroedingers equation used by spectroscopists to predict photon wavelength from molecule (extended orbital) size via the 1 dimensional box approximation? (I notice that you are a Chemist.................)

Thank you. This is very good.

Nice video. Could be brilliant if you can proof it with calculus.

@19:59 There's a mistake: It's "100 times x percent", not x percent! Biggest trip-hazard with percentages that there is: forgetting that it's a hundredth-factor!

You have the same periodic table poster as me! Mine was a gift from my grandpa who was a chemist.

Every exponential function F has pair of functions of which one of them has smaller factor (base) and it represents instantaneous growth rate of the function F, and the other one has bigger base (factor) which represents continuous growth factor of function F. Thus function's instantaneous growth rate is it's instantaneous counterpart's discrete growth rate i.e: 1.051278^x have instantaneous growth rate of 5 %, the discrete rate of (1.05^x) And any 2 exponential functions' instantaneous growth rates are proportional to the exponential ratio of their factors: f(x) = a^x g(x) = b^x b = a^r r = log(b)/log(a) = ln(b) if instantaneous growth rate of f(x) is p: then for g(x) it's equal to r*p. Explanation with derivatives: b = a^r then g(x) = b^x = a^rx = (a^x)^r = (f(x))^r (f(x) to the pow r). And instantaneous growth rate is actually a constant that occures in the derivative of exponential function which is for f(x) is simply f'(x) = k1*f(x), for g'(x) acrrording to chain rule is: g'(x) = g(x) * k2 ((f(x))^r)' => r*f(x)^(r-1)*f'(x) = r*f(x)^r/f(x)*f(x)*k1 => r*g(x)*k1 = g(x) * k2 => r*k1 = k2 If U want to why growth rate is actually derivative for exponential functions watch 3Blue1Brown's video (3:57): th-cam.com/video/m2MIpDrF7Es/w-d-xo.html I could'n yet figured out proportionality relationship between discrete and continuous growth rates of functions. This trio of functions ..... I(x) <=> D(x) <=> C(x) ...... chained in both direction infinitely. Every single one of them is instantaneous equivalent of the one on it's right and continuous equivalent of the one on it's left. In other words, every single function has instantaneous equivalent on it's left and continuous equivalent on it's right.

Since when does Exponential imply growing really fast?

so underrated, this needs more views

dude, you are incridibly awsome person

Excellent, Excellent, EXCELLENT video!!!

On release of ammonia slowly get diamnonium and monoammoniun phosphates. You could regenerate the triammonium with phosphoric acid once it gets old

the way i semi-formally proved the theorem was sort of like this: (click read more if you want to see it, don't click if you want to figure out yourself) (i'll use ellipses to indicate that a function or vector could continue to have any amount of variables/components) first off, dr = r'(t)dt = <x'(t)dt, y'(t)dt, … > = <dx, dy, … > ∇f = <∂f/∂x, ∂f/∂y, ... > ∇f•dr = ∇f•r'(t)dt= (∂f/∂x)dx + (∂f/∂y)dy + … a function's complete differential is equal to the sum of its partial derivatives, each multiplied by their corresponding differentials (e.g. (∂f/∂x)dx or anything similar) and the value of this dot product comes out to be in just the right form of this total differential so ∇f•dr = df now, before we move on, recall that we want to take the values of f at certain points plugging in t_0 or t_f alone won't do the job since we're talking multivariable here, but if we can find f in terms of t, that'll work so let's find f(r(t)) this will change f(x, y, … ) into f(x(t), y(t), … ) so now we can evaluate f at the t values now let's get back to the integral: we already know that by the FTC (or by the Generalized Stokes' Theorem) that the integral over an interval of the derivative of a function is equal to the original function at the bounds ∫_C ∇f•dr = ∫_{t_0} ^{t_f} df = f(r(t)) | _{t_0} ^{t_f} = f(r(t_f)) - f(r(t_0)) (the _{} ^{} indicates the bounds) and there we have it ∫_C ∇f•dr = f(r(t_f)) - f(r(t_0))

Brilliant stuff!

Yet another awesome video!

E😫

e just a number no a curve please explain to each other

Fantastic video. When I took real analysis I suddenly realized the proofs of theorems about generalized sets were outlined exactly in my elementary algebra and calculus texts in one variable.

Great explanation. I noticed you started saying _zero_ and _point_ instead of _o_ and _dot,_ congratulations!

Just magnificent! Thanks!!

is this taken in pimentel hall? go bears

ime impressed you are something else 😊😊👍👍

😂

It is also unfortunate that you took the bacterium reproducing as an example for "self-referential growth". Because, other than "compound interest rates" (8:38...9:41) bacteria are counted with whole numbers: 1->2->4->8->16..., while interest rates are represented, as real numbers. There are serious mathematical implications: we can not integrate, differentiate find the maximum/minimum, and importantly find the limes as n-->oo for the discrete numbers of bacteria, like it is nonsense, when 2 bacteria would reproduce pi-number of bacteria, or infinite number of bacteria in between!! The foolish chemists usually make the same mistake, when they counted their atoms/molecules with whole numbers and go ahead to apply the maths for real numbers!

Your equation at (13:25..13:32): (lambda^(x) = 1.05, finding x) does not make sense at all. Lambda is per definition a limit value of an infinity series lambda = lim (1 + r/n)^n = 1.05 ..............n->oo So, for n=100,000 ; 10,000 ; 1,000 ; 100 we got: r= 0.048790176 ; 0.048790283 ; 0.04879135 ; 0.0488020

Bravo. It’s always nice to learn another way of understanding something (that you thought you understood).

2:05 If df/dx is not a quotient then at 3:29 why do we take df/dx as slope (which is equal to tan theta)?

Excellent explanation - thanks! Minor one at 19:59: e^x is not self-growth at x % but x*100 %.

The information you shared is something maybe 1 out of 50.000 bachelor's graduates worldwide know, despite almost all being exposed to calculus or college algebra in their lifetime. I am assuming that even a very big percentage of college math teachers also won't have the intuition within this video. In ALL classes they teach e as a random universal number that we found from continuous interest and eventually found in other places, and NOT what it really was all along. Thank you so much, videos like these should put even the famous universities to shame. Just 20 minutes and such a beautiful chunk of info

The master ..BIg Thanks .

This is highly interesting, could you make a chemwalk about potential chemistry ? Thanks for sharing your knowledge!

I've got a one-sentence description for "e". It goes as: "The number e helps quantify the decay rate for simple dissipative processes in nature". There are countless examples for these so-called "simple dissipative processes", which behave in an asymptotic fashion. - The time-rate temperature decrease of a given volume of hot liquid (a cup of coffee). - The time-rate level decrease of water in a bathtub after the plug is removed from the drain. - The time-rate amplitude decrease in a mechanical oscillation system (mass-spring, pendulum, a swing, vibrating string under tension, etc.).

Tbh I really enjoy ur chem walkthroughs 🎉

There's a slight problem with your opening screen. Four constants are shown, all but the third of which are pure numbers. Planck's constant, h, is not a number; it's an angular momentum. So unlike i, π, and e, its numeric value depends on the choice of physical units, which from the point of view of physics, is arbitrary. The value given here is in the "mks" system, and so, needs to be 'finished' with "kg•m²/s." Also, at the 20-min mark, eˣ isn't for x%, but for 100x% growth rate. Fred

It wouldn’t be a calculus video without someone bringing up +c Edit: at 15:32 technically a constant would have been deleted by the derivative

2.71828182846^π√-1 +1≠0