Just saw this video only now. It is really useful, I completely missed this point. Yes, my high school time was long ago but still it was worth recapping this topic.
We should add zero to be able to collect the terms and separate fractions I found in the internet how to solve Rubic's cube by LBL method which is the easiest one Can we find any mathematic problems involving Rubic's cube ?
One thing I get confused is Newton's f prime notation drops the dx. But Liebnez always keeps the dx. Then when we try to do integral we need to write dx back to f prime. Does anybody know why that is? And
There is also product rule for higher derivatives It looks like binomial expansion but instead of powers we have derivatives You can prove it by induction As an example: Calculate d^n/dt^n f(x,t) where f(x,t) = exp(xt)cos(sqrt(1-x^2)t) (f(x,t) is exponential generating function of Chebyshev polynomials) This is good example because d^n/dt^n exp(xt) = x^nexp(xt) d^n/dt^n cos(sqrt(1-x^2)t) = (sqrt(1-x^2))^{n}cos(pi/2*n + sqrt(1-x^2)t) Could you record video about it ?
Here Wikipedia claims that exponential generating function of Chebyshev polynomials is exp(xt)cosh(sqrt(x^2-1)) but this version needs purely imaginary argument for hyperbolic cosine because x in [-1;1] so trigonometric cosine suits better
I watched a professor from MIT show this proof but he botched it totally so I could not understand him he did not make a mistake but he did not place emphasis on adding and subtracting "something" that is the why of it. Of course this proof we take for granted is a stroke of genius I am wondering how Newton proved this that is how his proof was unsatisfactory and Yes will check your web site like to see a proof of rubrics cube!
Explaining brilliantly
please do make the video on the rubrics cube, would love it
Just saw this video only now. It is really useful, I completely missed this point. Yes, my high school time was long ago but still it was worth recapping this topic.
I love your videos, well explained!👌
Been a year man
Has the video on rubic's cobe dropped??
We should add zero to be able to collect the terms and separate fractions
I found in the internet how to solve Rubic's cube by LBL method which is the easiest one
Can we find any mathematic problems involving Rubic's cube ?
Thank you so much, I'm learning a lot from your videos
Great video, but how are you sure that product of a limit is equal to the limit of the product?
If the limits are finite, that's a limit law.
One thing I get confused is Newton's f prime notation drops the dx. But Liebnez always keeps the dx. Then when we try to do integral we need to write dx back to f prime. Does anybody know why that is? And
There is also product rule for higher derivatives
It looks like binomial expansion but instead of powers we have derivatives
You can prove it by induction
As an example:
Calculate d^n/dt^n f(x,t)
where f(x,t) = exp(xt)cos(sqrt(1-x^2)t)
(f(x,t) is exponential generating function of Chebyshev polynomials)
This is good example because
d^n/dt^n exp(xt) = x^nexp(xt)
d^n/dt^n cos(sqrt(1-x^2)t) = (sqrt(1-x^2))^{n}cos(pi/2*n + sqrt(1-x^2)t)
Could you record video about it ?
Here Wikipedia claims that exponential generating function of Chebyshev polynomials is exp(xt)cosh(sqrt(x^2-1))
but this version needs purely imaginary argument for hyperbolic cosine because x in [-1;1] so trigonometric cosine suits better
👌👌👌😍😍
Awesome!
I watched a professor from MIT show this proof but he botched it totally so I could not understand him he did not make a mistake but he did not place emphasis on adding and subtracting "something" that is the why of it. Of course this proof we take for granted is a stroke of genius I am wondering how Newton proved this that is how his proof was unsatisfactory and Yes will check your web site like to see a proof of rubrics cube!
64th view, really nice number in that iirc it's. the lowest number that is both a perfect cube and a perfect square (besides 1 of course) great video!
64 is the smallest number with exactly 7 divisors 👌🤣
the rubrics cube and then chess
22nd view, 5th like😗