Відео

I was having a hard time visualizing line integrals- But now it makes so much sense! Great video, thanks for uploading!

e = 1/0! + 1/1! + 1/2! .............

What iPad app are you using?

Nice! This explains why the exponential map appears even when you’re not working with numbers anymore

Thank you for making it so clear and simple. Appreciated.

The way you hold the pen is just awful. It doesn't let to see what you are writing

Thermodynamics always had this smell of engineering to it, where the goal is to assemble machineries out of bags of molecules and exploit any pattern in the system that is not heat.

I oddly couldn't take the guy seriously because he's holding a clip-on mic in his hand for some reason

21:38 you bet!

Ok, I'll need to watch that a few more times and with a pen and paper. Tell me, why does e come on when making a complex circle?

I tried to educate 3m to multiply the money in my bank account but they did not have the necessary algebra skills to get the right answer.

i want to know the app you were writing in, if it is an app

It was a useful explanation that added to my knowledge, thank you for such educational videos, it helped to improve human knowledge and science.

awsome explanation to help understanding concepts

just a minor nit pick at 8:00, the projection is divided by the norm squared. *b* dot *a* over norm *a* is only the component of *b* in *a* 's direction. In other words, how much the unit vector in *a* direction is scaled. Hence, the extra division by norm of *a*

I don't think there is any reason at all to bring the approximation into it. The other stuff is great. But I think I can do better. I'm going to try and slap something together.

The easiest way to describe pi: It’s half tau.

I wish I had been presented to multivariable functions during High-School

This is crazy stuff...... Blown up my mind

I worked for a bank where savings account interest was compounded continuously. I used both Euler’s Number e and natural log ln quite frequently. Your explanation made sense to me. Next time you are talking to a banker ask for a proof of how your savings interest (Annual Percentage Yield) was determined. I bet no one in the bank can do the calculation let alone explain it.

Too much complicated

Fail.

The fact, that the language of the Math is not comprehensive to me, makes me sad.

scalability of large numbers by a factor, decimal converter? Used highly in diff eq, the visual helps, thanks, now how to upscale control theory into life?

Up until your discovery of constant-variable lambda I felt I was with you. From that point on I would need much more graduation. Very unfortunately I lost you from that point on. David Lixenberg

Tipical american: all about money.

Isn't dr/ds the unit tangent vector, whilst dr/dt the actual tangent vector ?

Hot Tip: (1.0000000001)^⁹ = e This is the smallest number taken to the exponent of its decimal place which is e, or 2.718.... Just add more zeros between the ones and take it to a higher exponent to get "e" with more decimal places.

E

Great video explaining e. I never thought e can be describe as "the self referential growth or decay" of itself. Nice!!!

Trancedental number like pi and square root of not perfect square

I'm sorry, but to ignore calculus in a video trying to give an intuition for e is a somewhat baffling move, since what makes e significant is its use in calculus (specifically for taking the derivative or anti-derivative of an exponential). Walking through how solving f'(x) = f(x) naturally leads to an exponential, and further showing that the base of that exponential is an exact constant, also gives an intuition on why it matters in chemistry and physics, after perhaps explaining why exponential equations are used to model how certain kinds of systems evolve (and how the past of them can be predicted) based only on some constants of the system and the current state.

This video is incredible. Keep up the good work!

Thanks for making this video sir, really helpful

very helpful！

No fire:(

I really wish the rest of this playkist was out my midterm is on Wednesday and this is so much more helpful AND ENTERTAINING than the explanations I've seen so far. SO MANY PEOPLE MAKE MATH BORING, you do not, thank you

This is extremely good

I think the basic line integral is a weighted sum of infinitesimal vectors. The result is again a vector. Taking the length of ds complicates matters, and generates a big discrepancy with line integrals in the complex analysis.

Time Dialation,continuum only correct at that exact moment,,benchmark that point x,2x+5 =8')

*Everytime*

Continuum has time dialation,only true at that exact moment new computing has up charge

π has a solution,a circle Alfa and Omega

Time dialation,only correct at that moment time is a continuum

X,2x+5=8')

1:06 nor is pi. Pi is irrational and cant be expressed as a ratio of two numbers.

Yet another rehashed bad way to teach e. Not knocking Foolish Chemist. It’s a good math video. We tend to teach math by backing into concepts from an historical perspective. Instead we should relegate the arduous path to discovery of things like e and i to a math history class. Now that we have a better understanding of these concepts we should start with a modern perspective.

E is a letter that represents a number of

So Euler's number is the same as natural log. 2.718281828459 ?

This is exactly how my tutor explained e