Where does “e” come from?

[@robharwood3538]

I love how you tied the *motivation* for finding e into this 'mystery' of having derivative/slope of 2^x being less than 2^x, whereas deriv/slope of 3^x is bigger than 3^x -- and then *drawing* this on the board. Very intuitive that there should be someplace in between where the deriv/slope is equal to the original curve.

[@Delan1994]

Great video Dr. Ali . Can you do Euler’s formulas next time . Thank you

[@BaljinderSingh-um3fy]

6:37 ln2 means log to base e He is explaining e with help of e Please explain

[@ishani-0897]

I'm a high school senior and I've liked the idea of being an engineer for quite some time but this last year has been very difficult personally. Then, a couple days ago I came across a few of your videos and my passion for engineering was reignited. No kidding. You literally came as a godsend. The knowledge you share and the way you share it is amazing! Thank you so so much for what you do!! ❤

[@andyd777]

Hang in there. You got this

[@ishani-0897]

​@@andyd777heyy!! Thanks so much for that!❤

[@anthonykamel]

This is amazing! Please do Euler‘s number next.

[@Dharma_kuppala]

“Wow, this is the most unique and clear explanation of exponential numbers I’ve ever seen on KZbin! You made it so easy to understand. Please make more videos like this-your teaching style is amazing!”❤

[@alithedazzling]

Wow, thanks! Will keep making more of these for sure!

[@BaljinderSingh-um3fy]

​@@alithedazzling6:37 ln2 means log to base e You are explaining e with help of e

[@kasratabrizi2839]

I remember in high school when i asked the math teacher where this e came from he looked at me as if I asked a stupid question and just said: "this is a constant and you shouldn't be focussed on that to much. Just now that it is there so we can use it for whatever concept we want to explain". It is amazing how many teachers crush the curiosity of a student and how many students end up not reaching their full potential because of the educational system. It is sad. Anyways, I am very happy that you explained this in simple terms and I finally understand this now.

[@JimmyMatis-h9y]

You suffer from the misconception that public schools exist to foster kids' potential. They're to mold kids into obedient & not question authority & the status quo. No judgment here, I used to suffer from the same.

[@kasratabrizi2839]

@@JimmyMatis-h9y I know man, it is very sad. I wonder how many genuises we have destroyed who could have done amazing things.

[@griffingutches8261]

I had similar experiences in public education. The vast majority of my teachers were lazy and stupid. I agree, it is sad.

[@BAKERSTSIR]

First I was like what was too hard for my teachers that made them not explain this for us, then I realised that it's not because it's simple, you're just a good teacher who can buil the way to reach the point. Thank you.

[@exo-580]

isaac from kenya,i likes your intuition Ali on every topic it's refreshing to hear you talk on the most neglected yet essential things to understand in engineering,much love here

[@macebio]

I do love the way you manage to explain things. Only those who really understand things can explain them so clearly. Chapeu

[@davido1632]

You've been one of the most underrated youtubers for engineering students for a long time. I am glad this video format is working well for you

[@alithedazzling]

Thanks for the support, it means a lot!

[@MrBartuzi]

Those explanation videos are amazing. You truly have a gift when it comes to teaching.

[@alithedazzling]

Wow, thank you!

[@navin2176]

Teaching ❌ Understanding✅

[@Krazy0]

nice video, I encourage fellow viewers to visualize what we had learned from the video in Desmos or some plotting program, it's really a nice way to make sure you've a solid understanding of the lecture, ty Ali.

[@alithedazzling]

I agree, visualization is essential for understanding!

[@head85]

May Allah bless you. I have always wondered where e came from! I'll learn all i can from you!❤

[@nihilisticnirvana]

your stuff is so interesting to watch! I'm in my gap year after high school rn and your videos keep me connected to math on my year off. nice! keep making videos

[@alithedazzling]

That's awesome, keep learning!

[@J007-x8j]

A Great Video with a Great Footbal T-Shirt.

[@elorarose7816]

UNDERSTANDING AND IMAGINATION IS MORE IMPORTANT THAN THE ABILITY TO LEARN

[@dhrubabanerjee9177]

Thank you so much. Felt like I got an early Christmas gift. Please would love the next video about euler identity and Fourier transform.🙏

[@alithedazzling]

Thanks! I'm already working on those!

[@ejmakela7525]

I saw a previous video where you asked if there was interest in a video on exponentials. Yes, I said. Totally worth the wait!

[@ejmakela7525]

FYI, I’m an adult with a kid, my skill set is limited to pre-algebra, yet I still understand a lot of what you’re teaching. As I’ve gotten older, my interest in numbers has only increased. Intuition, curiosity, and a willingness to break convention are now the basis for how I approach learning mathematics.

[@alithedazzling]

glad you like the style of the videos! they will keep coming :)

[@sothisishowitreallyends]

I've watched a handful of these chalkboard style videos you've made and they continue to get better and better. Thanks for making em' and hope you keep it up

[@Jeremyduru14]

Amazing video man as always, This concept is not well taught but it has so many applications in all of Engineering and Science (Senior Mechanical Engineering Student at Stony Brook)

[@Rayan-lv9lg]

Allahumma Barik Brother keep it up

[@alinaddaf2474]

after years, now I underestand what e is. you are an amazing teacher. thank you for this video.

[@AlexAmStart123]

I'm studying Materials Science & Engeneering and you're helping me a lot with understanding the math part of it, in wich our prof kind of sucks to explain it

[@saharshsinghania1315]

Godsend! Exactly what I've been looking for to understand FFTs

[@ibrahimyt6990]

We'd love a video explaining Fourier's transform, excellent demonstration!

[@pyb.5672]

Very intuitive explanation. Well done as always. Love the minimalist series on the blackboard.

[@alithedazzling]

Glad you liked it!

[@johnfox9169]

Yes, please make a video or two on the Fourier Transform!!

[@swizzbeats1212]

Love your videos Ali, keep up the great work! :)

[@Parsa0o0i]

Thanks man. I really love it. im 15 from iran❤

[@Anonimus-96]

Thank you very much,Sir!

[@TenQYT]

Great explanation. I would like you to move with Euler's equation. I have no clue why that just became a circle.

[@marcocardinale7800]

Very good video! You could also have used the compound interest. I am waiting for the next video ;)

[@insell-l6d]

ure explanation is top notch pls u have a natural gift for communication big concepts with clear words

[@aeko6350]

ur so good at explaining things

[@Singh54321]

No words sir, just wow 🤯

[@johnstuder847]

Thanks Ali, another great video. You mentioned the complex exponential. I would definitely like to see a video about that. You might want to review the GoldPlatedGoof video ‘Fourier for the rest of us’. He pulls a lot of ideas together to explain Fourier in a very intuitive and practical way. Thanks again!

[@BKNeifert]

You know what, I see that same thing with circles and squares on parameter to area. That's interesting. So you're saying e describes the point where the area would be at equilibrium with the parameter? Like on a circle and square it's a line of 4. I wonder if that plays any role in figuring that out? Oh, that makes perfect sense now. You just helped me understand Euler's identity a little better. e^ipi=-1 because e creates equilibrium. The Pi creates a hemisphere, and the i puts it in a negative dimension, making it equal 0 if you add it, because the e makes equilibrium so the two hemispheres subtract. It doesn't work for other numbers, just like my 4 line doesn't work for shapes other than squares and circles. I just learned it has to do with sine and cosine, and I understand that too. Because if you calculate sine through a series it's going to equal pi, and then the i makes it work backward. Of course, being in three dimensions, I just visualize it as a hemisphere, but should probably visualize it as a circle now, as it's working through sine, and a circle has different geometry than a sphere.

[@einsteinwallah2]

4:20 independent function? 3x for 5 is dependent it is 3x for 4 plus 3 ... it is much useful to to teach e as limit of (1 + 1/n)^n as n is increased without restriction and it has nice interpretation also of continuously compounded interest earning financial instrument

[@harley6659]

Amazing video. Very helpful insight. I'm always annoyed by e being explained with money analogies, never thought of it as an equilibrium.

[@alithedazzling]

most people who use the money analogy don't deeply understand e

[@tommcwilliams1072]

The cyclic nature of e^ix comes from the cyclic nature of i: i^2 = -1, i^3 = -i, i^4=1, i^5 = i, etc.

[@tumi3348]

I feel like talking about how the equilibrium point where the derivative is the function it self falls a little short. It revolves around ln(e)=1 and then you could ask, "why is ln(e)=1" and why ln(x) is the antiderivative of 1/x. I'd like to understand why exactly e is the base of the natural logarithm.

[@jh_esports]

We got Ilkay Gündogan explaining math in a Real Madrid jersey before GTA6

[@Krenneth]

NO WAY he looks like gundogan

[@Yassine-sami-1]

This e is such a special number, please keep going. 🙏

[@saripallijitendra3573]

This guy needs to start a Math Channel ! Can't imagine if only Lin Alg, Probability, Calculus were explained like this.

[@Attaa0011]

You are very talented mashallah. Keep it going ❤.

[@alithedazzling]

Thanks, appreciate it!

[@mushqazi9852]

Bro. Really wonderful. I apprecite you.

[@alithedazzling]

It's my pleasure

[@TheZombieGAGA]

brilliant video ! thank you

[@sergek6943]

From your video on i I know i represents rotation (brilliant!)👏👏👏 Since for e^ix acceleration of rotation (derivative of function) equals to the function itself we are getting a perfect circle, not a spiral. That's what my intuition is telling me. I would really love to see your explanation. And your favorite prove of Euler's formula, please-please-please🙏.

[@insell-l6d]

impaccable explanation as always tysm ali could u pls do a vid abt derivatives

[@insell-l6d]

like on a deeper level i mean intuitively resonate with it not as its been taught in highschool

[@fizisistguy]

Yes, I have been very unable to find an intuitive explanation of where Euler's formula comes from.

[@DistortedV12]

they should replace doomscrolling with videos like this. Super clear and wish my teacher taught it this way back in highschool/undergrad

[@AbdullahEzzat-x3g]

I am so happy to see some Arabic person who is interested in science , Dr. Ali.😊

[@MubashirAhmed-i9r]

When I first learned that the derivative of e^x is e^x itself I wondered that why this happens and then I thought that some function grows and decays with constant rate of 2.71828 and if you take the rate of change that will always be equal to 2.71828. Btw nice explanation and looking forward to see a video on Euler's formula.

[@mh-ht2fp]

I like to think of "e" as a growth constant where its similar to the other constants such as gravitational constant or electric constant. So, it makes sense that the derivative of the growth constant, is the growth constant itself in the case of e^x.

[@UltraSteaKME]

A great lesson again! Absolutely, it would be amazing to see FFT and all its related topics decrypted through your eyes. Math should always be taught by engineers 😜

[@mohamdzombie5497]

It comes from Markiplier saying it

[@AarnavGrover]

Thanks for the great video! Can you explain imaginary exponents in your next video and the derivation of Euler's formula, as stated at the ending of the video?

[@aparajitaghosh8614]

Hey, love your explanations of concepts in each video. Can you also explain gauss theorem, lorentz force and lenz's law? Thanks

[@ThôngNguyễnHoàng-p3k]

Wow, thanks sir. Please make videos on Fourier and Talor transforms.

[@buen0_]

A video on Eulers formula would be great. I learned it in an EE class but it was never explained too well and I don’t totally understand it

[@robberlin2230]

My greatest achievement at university was to boldly define e as the number whose natural log = 1 I merely repeated the lecturers own comment 2 weeks before, which he forgot about and labelled me a legend

[@KC-hk2ub]

Yes please, whatever steps are required before learning the fourier transform, do them

[@aumbhise]

Will be waiting for Euler's formula 🙂

[@wus9472]

Great video,please continue in steps.

[@andyd777]

Great video bro. Would love to understand Euler’s equation better. Cheers

[@karimwalid-wg7xo]

Excellent video. I’m a junior ECE student and never knew that lol 😂

[@NABAJYOTIMOHAPATRA-i1f]

The time constant for a RC circuit is defined as the time required by the capacitor to discharge to 1/e times of its initial value . But what made the people consider 1/e as the deciding factor for the definition of Time Constant ; I mean people could have chosen some whole number like "70% or 65% of the initial value" rather than considering an irrational number "e".???

[@mecanuktutorials6476]

I haven’t looked at control systems since my undergrad but I was reviewing this after looking at your comment. The time constant is the reciprocal of the cutoff frequency of a filter, which is where it experiences a 3dB drop and starts attenuating a signal. If we apply a signal below the cutoff frequency, the signal won’t attenuate for a LPF. But if we apply a signal higher than the cutoff frequency it will attenuate very sharply. Now, the point of interest is where T = 1/ (f) because it will yield: E = E0 * e ^ (-j 2 pi fc t) E = E0 * e ^ (-j 2 pi t / T) E / E0 = e ^ (-j 2 pi t / T) If t == T (aka: the 3dB point), E/E0 = e ^ (-j 2 pi) E/E0 = 1 / e or something like that. I didn’t really separate into real and imaginary for this last piece. But: cos(2 pi) + j sin(2pi) => cos(2 pi) = 1

[@tommcwilliams1072]

"height = slope = acceleration = etc" is the quick way to describe the core feature of e^x

[@johnstuder847]

Are you saying: since derivatives of e^x are equal, that position, velocity and acceleration can be equal? That would be an interesting take on this. Do you make videos?

[@tommcwilliams1072]

BTW, e "comes from" the world of finance; it was bankers who discovered it doing continuously compounded interest. Bernoulli got credit for publishing it.

[@ShivanshTiwari-yn8wd]

Thank you for explaining, but I want to point out something, I have watched previous videos, and they are mazing, but in this video, I feel less clarity. I understood till 9:53, but after that I didn't absorb much. But thank you for making such videos ☺

[@abhishekgrover-pv1ic]

Nice explanation

[@eugenia1286]

I would really appreciate a video on Euler's formula :)

[@BB-ko3fh]

can you do a deep dive of Fourier transform explaining each section in this level of detail (not overlooking the intuition, as that is the main learning)

[@Derecichei999]

I would love to get to understand eulers formula! Thanks for this video!

[@itsmegaurav171]

Great Video!

[@kzavera]

Great video! Fouriers transform next

[@ajaykulkarni576]

What's so special about knowing e if the derivative of the function e^x is the function itself? Why is it important for a function to have its derivative equal to itself? Also, could you explain why e^(iθ) forms a circle?

[@torontawy]

You did not cover the story right: here is the e-story: 1- Euler connected the three different Centers of a triangle and found out the proportion between them is always e:1. 2- when he did the limit of (1 + 1/n)^n it was e. 3- when he solved the 3 envelope problem the solution was e .

[@manuelodabashian1089]

I would like to know about Euler's formula more

[@NameAhmad182]

The probleme is some doctors and teachers don't like to dive deeper with these stuffs how you discover these things is that all done by yourself or someone help you.plz answer me dr.ali

[@ramyad5]

Thank you Doctor

[@masaters8345]

Y'know your two complex number vids? I was thinking and and y'know how if you get imaginary roots of a polynomial then plot those on a complex plane AND take the way of thinking about complex planes with the hand/finger analogy, can these two things be related? Or are simply two different uses of the same mathematical construct?

[@alithedazzling]

yes they are related for sure! they are essentially 2 ways of describing the same thing

[@masaters8345]

@alithedazzling right okay, this may sound dumb but I understand how being able to describe "the part you can currently measure and part you can't currently measure" (your hand/finger analogy) is useful But how is knowing the complex roots of a polynomial useful? other than simply being able to get an answer? Also please continue with e^i*theta and how that represents a circle instead of exponential it's interesting, I was taught it in the cis(theta) form, which is just cos + i sin.

[@Singh54321]

Please explain that equation.✍️

[@nikhilkartha]

uhh.. you can explain f_n(x) = n*x as a dependent function f_n(x) = f_{n-1}(x) + n, I don't know what you are trying to say there at 4:25

[@chillydill4703]

Fantastic explanation! Just using a simple table like this explains a lot. And then when seeing Eulers formula, I was like ahh that makes a lot of sense now since we are rotating in the imaginary plane when using e^i𝜽. Also, now it makes sense of ln(e) is just e.

[@worldnotworld]

Dagnabbit, I love a good old fashioned blackboard...

[@justgold1]

Thanks bro you explain all the stuff that wouldnt make sense 🙏

[@AlexMyM]

Nice shirt. ❤

[@NameAhmad182]

Woow absolutely interreseted

[@zika9688]

I'm praying the Fourier tansforms video comes out before my final :')

[@alithedazzling]

when's your final?

[@zika9688]

@alithedazzling On the 17th of January :')) (Signals and Systems exam)

[@alithedazzling]

@@zika9688 you'll get a few videos before then :)

[@zika9688]

@@alithedazzling:DDD

[@hmga1999]

Yes please, develop the origin of Euler's equation, please 🙏🏽

[@aneraxxmusic2343]

Nice real madrid jersey

[@Oskar0424]

We were at UB at the same time...

[@camryhsalem5139]

Very hard to pause ⏸️ your video ❤

[@meqs700]

Ali, can we keep on doing maths or physics after finishing electrical engineering degree?

[@alithedazzling]

yes

[@Anonimowany1]

I cant grasp the fact that the derivative of a function can grow faster than the function itself. It seems so counter-intuitive to myself. I always thought and felt that any derivation will always only be growing at the same rate or slow than the original function. Any intuitive way to explain this?

[@Krenneth]

HALA MADRID ❤

[@Lukas14-lg5dq]

do programming combined with advanced math videos plz

[@P6R9O]

I hope you do a video about Taylor series

[@qti4874]

Can you give us some free resources to learn telecommunications